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- La ecuación:
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Ecuación 4-x/7=x/9
-
Ecuación z^4=1
-
Ecuación 5x+15=x-1
-
Ecuación 2+3x=-7x-5
- Expresar {x} en función de y en la ecuación:
- -17*x-15*y=-17
- 12*x-20*y=10
- -20*x-13*y=15
- 9*x+14*y=-10
-
Expresiones idénticas
- exp(cuarenta y cinco *x)= cuarenta y ocho / doscientos cincuenta y dos
- exponente de (45 multiplicar por x) es igual a 48 dividir por 252
- exponente de (cuarenta y cinco multiplicar por x) es igual a cuarenta y ocho dividir por doscientos cincuenta y dos
- exp(45x)=48/252
- exp45x=48/252
- exp(45*x)=48 dividir por 252
-
Expresiones con funciones
- Exponente exp
- exp(x-2)-log(x+2)=0
- exp(x*21)
- exp(i*x)=1-i
- exp(x)-5cosx=0
- exp(-456x)=0,25
exp(45*x)=48/252 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación:
$$e^{45 x} = \frac{4}{21}$$
o
$$e^{45 x} - \frac{4}{21} = 0$$
o
$$e^{45 x} = \frac{4}{21}$$
o
$$e^{45 x} = \frac{4}{21}$$
- es la ecuación exponencial más simple
Sustituimos
$$v = e^{45 x}$$
obtendremos
$$v - \frac{4}{21} = 0$$
o
$$v - \frac{4}{21} = 0$$
Transportamos los términos libres (sin v)
del miembro izquierdo al derecho, obtenemos:
$$v = \frac{4}{21}$$
Obtenemos la respuesta: v = 4/21
hacemos cambio inverso
$$e^{45 x} = v$$
o
$$x = \frac{\log{\left(v \right)}}{45}$$
Entonces la respuesta definitiva es
$$x_{1} = \frac{\log{\left(\frac{4}{21} \right)}}{\log{\left(e^{45} \right)}} = \frac{\log{\left(\frac{4}{21} \right)}}{45}$$
$$e^{45 x} = \frac{4}{21}$$
o
$$e^{45 x} - \frac{4}{21} = 0$$
o
$$e^{45 x} = \frac{4}{21}$$
o
$$e^{45 x} = \frac{4}{21}$$
- es la ecuación exponencial más simple
Sustituimos
$$v = e^{45 x}$$
obtendremos
$$v - \frac{4}{21} = 0$$
o
$$v - \frac{4}{21} = 0$$
Transportamos los términos libres (sin v)
del miembro izquierdo al derecho, obtenemos:
$$v = \frac{4}{21}$$
Obtenemos la respuesta: v = 4/21
hacemos cambio inverso
$$e^{45 x} = v$$
o
$$x = \frac{\log{\left(v \right)}}{45}$$
Entonces la respuesta definitiva es
$$x_{1} = \frac{\log{\left(\frac{4}{21} \right)}}{\log{\left(e^{45} \right)}} = \frac{\log{\left(\frac{4}{21} \right)}}{45}$$
Respuesta rápida
[src]
/ 44\
| --|
| 2/45 45|
|2 *21 |
x1 = log|----------|
\ 21 /
$$x_{1} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)}$$
/ 49 44 43 44 43 44\ / 44\
| -- -- ___________ -- -- -- --| | --|
| 90 45 / ___ 2/45 90 45 2/45 90 ___ 45| | 2/45 45|
|- 2 *21 *\/ 5 - \/ 5 + 3*2 *3 *7 + 3*2 *3 *\/ 5 *7 | |2 *21 |
x2 = I*atan|-------------------------------------------------------------------| + log|----------|
| 44 44 49 43 44 | \ 21 /
| -- -- -- -- -- ___________ |
| 2/45 45 2/45 ___ 45 90 90 45 / ___ |
\ 2 *21 + 2 *\/ 5 *21 + 3*2 *3 *7 *\/ 5 - \/ 5 /
$$x_{2} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \operatorname{atan}{\left(\frac{- 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{5 - \sqrt{5}} + 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} + 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}}}{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5} + 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{5 - \sqrt{5}}} \right)}$$
/ 49 44 43 44 43 44\ / 44\
| -- -- ___________ -- -- -- --| | --|
| 90 45 / ___ 2/45 90 45 2/45 90 ___ 45| | 2/45 45|
|2 *21 *\/ 5 - \/ 5 - 3*2 *3 *7 - 3*2 *3 *\/ 5 *7 | |2 *21 |
x3 = I*atan|-----------------------------------------------------------------| + log|----------|
| 44 44 49 43 44 | \ 21 /
| -- -- -- -- -- ___________ |
| 2/45 45 2/45 ___ 45 90 90 45 / ___ |
\ 2 *21 + 2 *\/ 5 *21 + 3*2 *3 *7 *\/ 5 - \/ 5 /
$$x_{3} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \operatorname{atan}{\left(\frac{- 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}} - 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} + 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{5 - \sqrt{5}}}{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5} + 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{5 - \sqrt{5}}} \right)}$$
/ 49 44 43 44 43 44\ / 44\
| -- -- ___________ -- -- -- --| | --|
| 90 45 / ___ 2/45 90 45 2/45 90 ___ 45| | 2/45 45|
|2 *21 *\/ 5 + \/ 5 - 3*2 *3 *7 + 3*2 *3 *\/ 5 *7 | |2 *21 |
x4 = I*atan|-----------------------------------------------------------------| + log|----------|
| 44 44 49 43 44 | \ 21 /
| -- -- -- -- -- ___________ |
| 2/45 45 2/45 ___ 45 90 90 45 / ___ |
\ 2 *21 - 2 *\/ 5 *21 + 3*2 *3 *7 *\/ 5 + \/ 5 /
$$x_{4} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \operatorname{atan}{\left(\frac{- 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} + 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{\sqrt{5} + 5} + 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}}}{- 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} + 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{\sqrt{5} + 5}} \right)}$$
/ 49 44 43 44 43 44\ / 44\
| -- -- ___________ -- -- -- --| | --|
| 90 45 / ___ 2/45 90 45 2/45 90 ___ 45| | 2/45 45|
|- 2 *21 *\/ 5 + \/ 5 + 3*2 *3 *7 - 3*2 *3 *\/ 5 *7 | |2 *21 |
x5 = I*atan|-------------------------------------------------------------------| + log|----------|
| 44 44 49 43 44 | \ 21 /
| -- -- -- -- -- ___________ |
| 2/45 45 2/45 ___ 45 90 90 45 / ___ |
\ 2 *21 - 2 *\/ 5 *21 + 3*2 *3 *7 *\/ 5 + \/ 5 /
$$x_{5} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \operatorname{atan}{\left(\frac{- 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}} - 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{\sqrt{5} + 5} + 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}}}{- 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} + 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{\sqrt{5} + 5}} \right)}$$
/ / 49 44 43 44 43 44\\ / 44\
| | -- -- ___________ -- -- -- --|| | --|
| | 90 45 / ___ 2/45 90 45 2/45 90 ___ 45|| | 2/45 45|
| |2 *21 *\/ 5 - \/ 5 + 3*2 *3 *7 + 3*2 *3 *\/ 5 *7 || |2 *21 |
x6 = I*|pi + atan|-----------------------------------------------------------------|| + log|----------|
| | 44 44 49 43 44 || \ 21 /
| | -- -- -- -- -- ___________ ||
| | 2/45 45 2/45 ___ 45 90 90 45 / ___ ||
\ \ 2 *21 + 2 *\/ 5 *21 - 3*2 *3 *7 *\/ 5 - \/ 5 //
$$x_{6} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \left(\operatorname{atan}{\left(\frac{3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} + 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{5 - \sqrt{5}} + 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}}}{- 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{5 - \sqrt{5}} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5}} \right)} + \pi\right)$$
/ / / 49 44 43 44 43 44\ \\ / 44\
| | | -- -- ___________ -- -- -- --| || | --|
| | | 90 45 / ___ 2/45 90 45 2/45 90 ___ 45| || | 2/45 45|
| |-\- 2 *21 *\/ 5 - \/ 5 - 3*2 *3 *7 - 3*2 *3 *\/ 5 *7 / || |2 *21 |
x7 = I*|-pi - atan|-----------------------------------------------------------------------|| + log|----------|
| | 44 44 49 43 44 || \ 21 /
| | -- -- -- -- -- ___________ ||
| | 2/45 45 2/45 ___ 45 90 90 45 / ___ ||
\ \ 2 *21 + 2 *\/ 5 *21 - 3*2 *3 *7 *\/ 5 - \/ 5 //
$$x_{7} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \left(- \pi - \operatorname{atan}{\left(- \frac{- 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}} - 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{5 - \sqrt{5}} - 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}}}{- 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{5 - \sqrt{5}} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5}} \right)}\right)$$
/ / 49 44 43 44 43 44\\ / 44\
| | -- -- ___________ -- -- -- --|| | --|
| | 90 45 / ___ 2/45 90 45 2/45 90 ___ 45|| | 2/45 45|
| |- 2 *21 *\/ 5 + \/ 5 - 3*2 *3 *7 + 3*2 *3 *\/ 5 *7 || |2 *21 |
x8 = I*|-pi + atan|-------------------------------------------------------------------|| + log|----------|
| | 44 44 49 43 44 || \ 21 /
| | -- -- -- -- -- ___________ ||
| | 2/45 45 2/45 ___ 45 90 90 45 / ___ ||
\ \ 2 *21 - 2 *\/ 5 *21 - 3*2 *3 *7 *\/ 5 + \/ 5 //
$$x_{8} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{- 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{\sqrt{5} + 5} - 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} + 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}}}{- 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{\sqrt{5} + 5} - 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}} \right)}\right)$$
/ / 49 44 43 44 43 44\\ / 44\
| | -- -- ___________ -- -- -- --|| | --|
| | 90 45 / ___ 2/45 90 45 2/45 90 ___ 45|| | 2/45 45|
| |2 *21 *\/ 5 + \/ 5 + 3*2 *3 *7 - 3*2 *3 *\/ 5 *7 || |2 *21 |
x9 = I*|pi + atan|-----------------------------------------------------------------|| + log|----------|
| | 44 44 49 43 44 || \ 21 /
| | -- -- -- -- -- ___________ ||
| | 2/45 45 2/45 ___ 45 90 90 45 / ___ ||
\ \ 2 *21 - 2 *\/ 5 *21 - 3*2 *3 *7 *\/ 5 + \/ 5 //
$$x_{9} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + i \left(\operatorname{atan}{\left(\frac{- 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \sqrt{5} \cdot 7^{\frac{44}{45}} + 3 \cdot 2^{\frac{2}{45}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} + 2^{\frac{49}{90}} \cdot 21^{\frac{44}{45}} \sqrt{\sqrt{5} + 5}}{- 3 \cdot 2^{\frac{49}{90}} \cdot 3^{\frac{43}{90}} \cdot 7^{\frac{44}{45}} \sqrt{\sqrt{5} + 5} - 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}} \sqrt{5} + 2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}} \right)} + \pi\right)$$
/ 44\
| --|
| 2/45 45|
4*pi*I |2 *21 |
x10 = - ------ + log|----------|
5 \ 21 /
$$x_{10} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} - \frac{4 i \pi}{5}$$
/ 44\
| --|
| 2/45 45|
2*pi*I |2 *21 |
x11 = - ------ + log|----------|
3 \ 21 /
$$x_{11} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} - \frac{2 i \pi}{3}$$
/ 44\
| --|
| 2/45 45|
2*pi*I |2 *21 |
x12 = - ------ + log|----------|
5 \ 21 /
$$x_{12} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} - \frac{2 i \pi}{5}$$
/ 44\
| --|
| 2/45 45|
2*pi*I |2 *21 |
x13 = ------ + log|----------|
5 \ 21 /
$$x_{13} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + \frac{2 i \pi}{5}$$
/ 44\
| --|
| 2/45 45|
2*pi*I |2 *21 |
x14 = ------ + log|----------|
3 \ 21 /
$$x_{14} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + \frac{2 i \pi}{3}$$
/ 44\
| --|
| 2/45 45|
4*pi*I |2 *21 |
x15 = ------ + log|----------|
5 \ 21 /
$$x_{15} = \log{\left(\frac{2^{\frac{2}{45}} \cdot 21^{\frac{44}{45}}}{21} \right)} + \frac{4 i \pi}{5}$$
/ ___________________________________________\
| / 43 43 |
| / -- -- |
/ / /pi\\\ | / 4/45 45 2/pi\ 4/45 45 2/pi\ |
| |sin|--||| | / 2 *21 *cos |--| 2 *21 *sin |--| |
| | \45/|| | / \45/ \45/ |
x16 = I*|-pi + atan|-------|| + log| / ------------------- + ------------------- |
| | /pi\|| \\/ 21 21 /
| |cos|--|||
\ \ \45///
$$x_{16} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{\pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{\pi}{45} \right)}}{21}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{45} \right)}}{\cos{\left(\frac{\pi}{45} \right)}} \right)}\right)$$
/ ___________________________________________\
| / 43 43 |
| / -- -- |
/ / /pi\\\ | / 4/45 45 2/pi\ 4/45 45 2/pi\ |
| |sin|--||| | / 2 *21 *cos |--| 2 *21 *sin |--| |
| | \45/|| | / \45/ \45/ |
x17 = I*|pi - atan|-------|| + log| / ------------------- + ------------------- |
| | /pi\|| \\/ 21 21 /
| |cos|--|||
\ \ \45///
$$x_{17} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{\pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{\pi}{45} \right)}}{21}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{45} \right)}}{\cos{\left(\frac{\pi}{45} \right)}} \right)}\right)$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /2*pi\\ | / 4/45 45 2/2*pi\ 4/45 45 2/2*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 45 /| | / \ 45 / \ 45 / |
x18 = - I*atan|---------| + log| / --------------------- + --------------------- |
| /2*pi\| \\/ 21 21 /
|cos|----||
\ \ 45 //
$$x_{18} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{2 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{2 \pi}{45} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{45} \right)}}{\cos{\left(\frac{2 \pi}{45} \right)}} \right)}$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /2*pi\\ | / 4/45 45 2/2*pi\ 4/45 45 2/2*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 45 /| | / \ 45 / \ 45 / |
x19 = I*atan|---------| + log| / --------------------- + --------------------- |
| /2*pi\| \\/ 21 21 /
|cos|----||
\ \ 45 //
$$x_{19} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{2 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{2 \pi}{45} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{45} \right)}}{\cos{\left(\frac{2 \pi}{45} \right)}} \right)}$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /4*pi\\ | / 4/45 45 2/4*pi\ 4/45 45 2/4*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 45 /| | / \ 45 / \ 45 / |
x20 = - I*atan|---------| + log| / --------------------- + --------------------- |
| /4*pi\| \\/ 21 21 /
|cos|----||
\ \ 45 //
$$x_{20} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{4 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{4 \pi}{45} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{45} \right)}}{\cos{\left(\frac{4 \pi}{45} \right)}} \right)}$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /4*pi\\ | / 4/45 45 2/4*pi\ 4/45 45 2/4*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 45 /| | / \ 45 / \ 45 / |
x21 = I*atan|---------| + log| / --------------------- + --------------------- |
| /4*pi\| \\/ 21 21 /
|cos|----||
\ \ 45 //
$$x_{21} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{4 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{4 \pi}{45} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{45} \right)}}{\cos{\left(\frac{4 \pi}{45} \right)}} \right)}$$
/ ___________________________________________\
| / 43 43 |
| / -- -- |
/ / /pi\\\ | / 4/45 45 2/pi\ 4/45 45 2/pi\ |
| |sin|--||| | / 2 *21 *cos |--| 2 *21 *sin |--| |
| | \9 /|| | / \9 / \9 / |
x22 = I*|-pi + atan|-------|| + log| / ------------------- + ------------------- |
| | /pi\|| \\/ 21 21 /
| |cos|--|||
\ \ \9 ///
$$x_{22} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{21}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{9} \right)}}{\cos{\left(\frac{\pi}{9} \right)}} \right)}\right)$$
/ ___________________________________________\
| / 43 43 |
| / -- -- |
/ / /pi\\\ | / 4/45 45 2/pi\ 4/45 45 2/pi\ |
| |sin|--||| | / 2 *21 *cos |--| 2 *21 *sin |--| |
| | \9 /|| | / \9 / \9 / |
x23 = I*|pi - atan|-------|| + log| / ------------------- + ------------------- |
| | /pi\|| \\/ 21 21 /
| |cos|--|||
\ \ \9 ///
$$x_{23} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{21}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{9} \right)}}{\cos{\left(\frac{\pi}{9} \right)}} \right)}\right)$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ / /7*pi\\\ | / 4/45 45 2/7*pi\ 4/45 45 2/7*pi\ |
| |sin|----||| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x24 = I*|-pi + atan|---------|| + log| / --------------------- + --------------------- |
| | /7*pi\|| \\/ 21 21 /
| |cos|----|||
\ \ \ 45 ///
$$x_{24} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{7 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{7 \pi}{45} \right)}}{21}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{7 \pi}{45} \right)}}{\cos{\left(\frac{7 \pi}{45} \right)}} \right)}\right)$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ / /7*pi\\\ | / 4/45 45 2/7*pi\ 4/45 45 2/7*pi\ |
| |sin|----||| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x25 = I*|pi - atan|---------|| + log| / --------------------- + --------------------- |
| | /7*pi\|| \\/ 21 21 /
| |cos|----|||
\ \ \ 45 ///
$$x_{25} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{7 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{7 \pi}{45} \right)}}{21}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{7 \pi}{45} \right)}}{\cos{\left(\frac{7 \pi}{45} \right)}} \right)}\right)$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /8*pi\\ | / 4/45 45 2/8*pi\ 4/45 45 2/8*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 45 /| | / \ 45 / \ 45 / |
x26 = - I*atan|---------| + log| / --------------------- + --------------------- |
| /8*pi\| \\/ 21 21 /
|cos|----||
\ \ 45 //
$$x_{26} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{8 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{8 \pi}{45} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{8 \pi}{45} \right)}}{\cos{\left(\frac{8 \pi}{45} \right)}} \right)}$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /8*pi\\ | / 4/45 45 2/8*pi\ 4/45 45 2/8*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 45 /| | / \ 45 / \ 45 / |
x27 = I*atan|---------| + log| / --------------------- + --------------------- |
| /8*pi\| \\/ 21 21 /
|cos|----||
\ \ 45 //
$$x_{27} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{8 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{8 \pi}{45} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{8 \pi}{45} \right)}}{\cos{\left(\frac{8 \pi}{45} \right)}} \right)}$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /2*pi\\ | / 4/45 45 2/2*pi\ 4/45 45 2/2*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 9 /| | / \ 9 / \ 9 / |
x28 = - I*atan|---------| + log| / --------------------- + --------------------- |
| /2*pi\| \\/ 21 21 /
|cos|----||
\ \ 9 //
$$x_{28} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{2 \pi}{9} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{2 \pi}{9} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{9} \right)}}{\cos{\left(\frac{2 \pi}{9} \right)}} \right)}$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /2*pi\\ | / 4/45 45 2/2*pi\ 4/45 45 2/2*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 9 /| | / \ 9 / \ 9 / |
x29 = I*atan|---------| + log| / --------------------- + --------------------- |
| /2*pi\| \\/ 21 21 /
|cos|----||
\ \ 9 //
$$x_{29} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{2 \pi}{9} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{2 \pi}{9} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{9} \right)}}{\cos{\left(\frac{2 \pi}{9} \right)}} \right)}$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /11*pi\\\ | / 4/45 45 2/11*pi\ 4/45 45 2/11*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x30 = I*|-pi + atan|----------|| + log| / ---------------------- + ---------------------- |
| | /11*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{30} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{11 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{11 \pi}{45} \right)}}{21}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{11 \pi}{45} \right)}}{\cos{\left(\frac{11 \pi}{45} \right)}} \right)}\right)$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /11*pi\\\ | / 4/45 45 2/11*pi\ 4/45 45 2/11*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x31 = I*|pi - atan|----------|| + log| / ---------------------- + ---------------------- |
| | /11*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{31} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{11 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{11 \pi}{45} \right)}}{21}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{11 \pi}{45} \right)}}{\cos{\left(\frac{11 \pi}{45} \right)}} \right)}\right)$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /13*pi\\\ | / 4/45 45 2/13*pi\ 4/45 45 2/13*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x32 = I*|-pi + atan|----------|| + log| / ---------------------- + ---------------------- |
| | /13*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{32} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{13 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{13 \pi}{45} \right)}}{21}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{13 \pi}{45} \right)}}{\cos{\left(\frac{13 \pi}{45} \right)}} \right)}\right)$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /13*pi\\\ | / 4/45 45 2/13*pi\ 4/45 45 2/13*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x33 = I*|pi - atan|----------|| + log| / ---------------------- + ---------------------- |
| | /13*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{33} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{13 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{13 \pi}{45} \right)}}{21}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{13 \pi}{45} \right)}}{\cos{\left(\frac{13 \pi}{45} \right)}} \right)}\right)$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ /14*pi\\ | / 4/45 45 2/14*pi\ 4/45 45 2/14*pi\ |
|sin|-----|| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| \ 45 /| | / \ 45 / \ 45 / |
x34 = - I*atan|----------| + log| / ---------------------- + ---------------------- |
| /14*pi\| \\/ 21 21 /
|cos|-----||
\ \ 45 //
$$x_{34} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{14 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{14 \pi}{45} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{14 \pi}{45} \right)}}{\cos{\left(\frac{14 \pi}{45} \right)}} \right)}$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ /14*pi\\ | / 4/45 45 2/14*pi\ 4/45 45 2/14*pi\ |
|sin|-----|| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| \ 45 /| | / \ 45 / \ 45 / |
x35 = I*atan|----------| + log| / ---------------------- + ---------------------- |
| /14*pi\| \\/ 21 21 /
|cos|-----||
\ \ 45 //
$$x_{35} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{14 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{14 \pi}{45} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{14 \pi}{45} \right)}}{\cos{\left(\frac{14 \pi}{45} \right)}} \right)}$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ /16*pi\\ | / 4/45 45 2/16*pi\ 4/45 45 2/16*pi\ |
|sin|-----|| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| \ 45 /| | / \ 45 / \ 45 / |
x36 = - I*atan|----------| + log| / ---------------------- + ---------------------- |
| /16*pi\| \\/ 21 21 /
|cos|-----||
\ \ 45 //
$$x_{36} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{16 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{16 \pi}{45} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{16 \pi}{45} \right)}}{\cos{\left(\frac{16 \pi}{45} \right)}} \right)}$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ /16*pi\\ | / 4/45 45 2/16*pi\ 4/45 45 2/16*pi\ |
|sin|-----|| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| \ 45 /| | / \ 45 / \ 45 / |
x37 = I*atan|----------| + log| / ---------------------- + ---------------------- |
| /16*pi\| \\/ 21 21 /
|cos|-----||
\ \ 45 //
$$x_{37} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{16 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{16 \pi}{45} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{16 \pi}{45} \right)}}{\cos{\left(\frac{16 \pi}{45} \right)}} \right)}$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /17*pi\\\ | / 4/45 45 2/17*pi\ 4/45 45 2/17*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x38 = I*|-pi + atan|----------|| + log| / ---------------------- + ---------------------- |
| | /17*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{38} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{17 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{17 \pi}{45} \right)}}{21}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{17 \pi}{45} \right)}}{\cos{\left(\frac{17 \pi}{45} \right)}} \right)}\right)$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /17*pi\\\ | / 4/45 45 2/17*pi\ 4/45 45 2/17*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x39 = I*|pi - atan|----------|| + log| / ---------------------- + ---------------------- |
| | /17*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{39} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{17 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{17 \pi}{45} \right)}}{21}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{17 \pi}{45} \right)}}{\cos{\left(\frac{17 \pi}{45} \right)}} \right)}\right)$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /19*pi\\\ | / 4/45 45 2/19*pi\ 4/45 45 2/19*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x40 = I*|-pi + atan|----------|| + log| / ---------------------- + ---------------------- |
| | /19*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{40} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{19 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{19 \pi}{45} \right)}}{21}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{19 \pi}{45} \right)}}{\cos{\left(\frac{19 \pi}{45} \right)}} \right)}\right)$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ / /19*pi\\\ | / 4/45 45 2/19*pi\ 4/45 45 2/19*pi\ |
| |sin|-----||| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| | \ 45 /|| | / \ 45 / \ 45 / |
x41 = I*|pi - atan|----------|| + log| / ---------------------- + ---------------------- |
| | /19*pi\|| \\/ 21 21 /
| |cos|-----|||
\ \ \ 45 ///
$$x_{41} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{19 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{19 \pi}{45} \right)}}{21}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{19 \pi}{45} \right)}}{\cos{\left(\frac{19 \pi}{45} \right)}} \right)}\right)$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /4*pi\\ | / 4/45 45 2/4*pi\ 4/45 45 2/4*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 9 /| | / \ 9 / \ 9 / |
x42 = - I*atan|---------| + log| / --------------------- + --------------------- |
| /4*pi\| \\/ 21 21 /
|cos|----||
\ \ 9 //
$$x_{42} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{4 \pi}{9} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{4 \pi}{9} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{9} \right)}}{\cos{\left(\frac{4 \pi}{9} \right)}} \right)}$$
/ _______________________________________________\
| / 43 43 |
| / -- -- |
/ /4*pi\\ | / 4/45 45 2/4*pi\ 4/45 45 2/4*pi\ |
|sin|----|| | / 2 *21 *cos |----| 2 *21 *sin |----| |
| \ 9 /| | / \ 9 / \ 9 / |
x43 = I*atan|---------| + log| / --------------------- + --------------------- |
| /4*pi\| \\/ 21 21 /
|cos|----||
\ \ 9 //
$$x_{43} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{4 \pi}{9} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{4 \pi}{9} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{9} \right)}}{\cos{\left(\frac{4 \pi}{9} \right)}} \right)}$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ /22*pi\\ | / 4/45 45 2/22*pi\ 4/45 45 2/22*pi\ |
|sin|-----|| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| \ 45 /| | / \ 45 / \ 45 / |
x44 = - I*atan|----------| + log| / ---------------------- + ---------------------- |
| /22*pi\| \\/ 21 21 /
|cos|-----||
\ \ 45 //
$$x_{44} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{22 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{22 \pi}{45} \right)}}{21}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{22 \pi}{45} \right)}}{\cos{\left(\frac{22 \pi}{45} \right)}} \right)}$$
/ _________________________________________________\
| / 43 43 |
| / -- -- |
/ /22*pi\\ | / 4/45 45 2/22*pi\ 4/45 45 2/22*pi\ |
|sin|-----|| | / 2 *21 *cos |-----| 2 *21 *sin |-----| |
| \ 45 /| | / \ 45 / \ 45 / |
x45 = I*atan|----------| + log| / ---------------------- + ---------------------- |
| /22*pi\| \\/ 21 21 /
|cos|-----||
\ \ 45 //
$$x_{45} = \log{\left(\sqrt{\frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \cos^{2}{\left(\frac{22 \pi}{45} \right)}}{21} + \frac{2^{\frac{4}{45}} \cdot 21^{\frac{43}{45}} \sin^{2}{\left(\frac{22 \pi}{45} \right)}}{21}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{22 \pi}{45} \right)}}{\cos{\left(\frac{22 \pi}{45} \right)}} \right)}$$
x45 = log(sqrt(2^(4/45)*21^(43/45)*cos(22*pi/45)^2/21 + 2^(4/45)*21^(43/45)*sin(22*pi/45)^2/21)) + i*atan(sin(22*pi/45)/cos(22*pi/45))
Respuesta numérica
[src]
x1 = -0.0368495128134118 - 2.51327412287183*i
x2 = -0.0368495128134118 - 2.0943951023932*i
x3 = -0.0368495128134118 - 1.25663706143592*i
x4 = -0.0368495128134118 + 1.25663706143592*i
x5 = -0.0368495128134118 + 2.0943951023932*i
x6 = -0.0368495128134118 + 2.51327412287183*i
x7 = -0.0368495128134118
x8 = -0.0368495128134118 - 3.07177948351002*i
x9 = -0.0368495128134118 + 3.07177948351002*i
x10 = -0.0368495128134118 - 0.139626340159546*i
x11 = -0.0368495128134118 + 0.139626340159546*i
x12 = -0.0368495128134118 - 0.279252680319093*i
x13 = -0.0368495128134118 + 0.279252680319093*i
x14 = -0.0368495128134118 - 2.79252680319093*i
x15 = -0.0368495128134118 + 2.79252680319093*i
x16 = -0.0368495128134118 - 2.65290046303138*i
x17 = -0.0368495128134118 + 2.65290046303138*i
x18 = -0.0368495128134118 - 0.558505360638185*i
x19 = -0.0368495128134118 + 0.558505360638185*i
x20 = -0.0368495128134118 - 0.698131700797732*i
x21 = -0.0368495128134118 + 0.698131700797732*i
x22 = -0.0368495128134118 - 2.37364778271229*i
x23 = -0.0368495128134118 + 2.37364778271229*i
x24 = -0.0368495128134118 - 2.23402144255274*i
x25 = -0.0368495128134118 + 2.23402144255274*i
x26 = -0.0368495128134118 - 0.977384381116825*i
x27 = -0.0368495128134118 + 0.977384381116825*i
x28 = -0.0368495128134118 - 1.11701072127637*i
x29 = -0.0368495128134118 + 1.11701072127637*i
x30 = -0.0368495128134118 - 1.95476876223365*i
x31 = -0.0368495128134118 + 1.95476876223365*i
x32 = -0.0368495128134118 - 1.8151424220741*i
x33 = -0.0368495128134118 + 1.8151424220741*i
x34 = -0.0368495128134118 - 1.39626340159546*i
x35 = -0.0368495128134118 + 1.39626340159546*i
x36 = -0.0368495128134118 - 1.53588974175501*i
x37 = -0.0368495128134118 + 1.53588974175501*i
x38 = -0.0368495128134118 + 0.418879020478639*i
x39 = -0.0368495128134118 - 0.418879020478639*i
x40 = -0.0368495128134118 + 0.837758040957278*i
x41 = -0.0368495128134118 - 0.837758040957278*i
x42 = -0.0368495128134118 + 1.67551608191456*i
x43 = -0.0368495128134118 - 1.67551608191456*i
x44 = -0.0368495128134118 - 2.93215314335047*i
x45 = -0.0368495128134118 + 2.93215314335047*i
x45 = -0.0368495128134118 + 2.93215314335047*i