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Ecuación 1/(x-3)^2-3/(x-3)-4=0
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Ecuación 9*(x-5)=-x
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Ecuación 13x+10=6x-4
- Ecuación x-y=1
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Expresiones idénticas
- tres *cos(z)+i*sin(z)= tres -i
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Expresiones semejantes
- z^12=sqrt(3)-i
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Expresiones con funciones
- Coseno cos
- cos(x)=(-1/2)
- cos((pi*(x-7))/3)=1/2
- cos(x)/5=-1
- cos(x)=(-1)/sqrt(2)
- cos(a-b)+sin(-a)sinb
- Seno sin
- sin(x)=-√2/2
- sin(4*x)=1
- sin(-x)=1
- sin(x)=sqrt2/2
- sin(2x)=sqrt(2)/2
3*cos(z)+i*sin(z)=3-i la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3*cos(z) + I*sin(z) = 3 - I
$$i \sin{\left(z \right)} + 3 \cos{\left(z \right)} = 3 - i$$
Gráfica
Respuesta rápida
[src]
/ / / ___ ___\\\ / / / ___ ___\\\
| |(6 + I)*\I + \/ 6 *\/ I /|| | |(6 + I)*\I + \/ 6 *\/ I /||
z1 = 2*re|atan|-------------------------|| + 2*I*im|atan|-------------------------||
\ \ 37 // \ \ 37 //
$$z_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)}$$
/ / / ___ ___\\\ / / / ___ ___\\\
| |(6 + I)*\I - \/ 6 *\/ I /|| | |(6 + I)*\I - \/ 6 *\/ I /||
z2 = 2*re|atan|-------------------------|| + 2*I*im|atan|-------------------------||
\ \ 37 // \ \ 37 //
$$z_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)}$$
z2 = 2*re(atan((6 + i)*(-sqrt(6)*sqrt(i) + i)/37)) + 2*i*im(atan((6 + i)*(-sqrt(6)*sqrt(i) + i)/37))
Suma y producto de raíces
[src]
suma
/ / / ___ ___\\\ / / / ___ ___\\\ / / / ___ ___\\\ / / / ___ ___\\\
| |(6 + I)*\I + \/ 6 *\/ I /|| | |(6 + I)*\I + \/ 6 *\/ I /|| | |(6 + I)*\I - \/ 6 *\/ I /|| | |(6 + I)*\I - \/ 6 *\/ I /||
2*re|atan|-------------------------|| + 2*I*im|atan|-------------------------|| + 2*re|atan|-------------------------|| + 2*I*im|atan|-------------------------||
\ \ 37 // \ \ 37 // \ \ 37 // \ \ 37 //
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)}\right)$$
=
/ / / ___ ___\\\ / / / ___ ___\\\ / / / ___ ___\\\ / / / ___ ___\\\
| |(6 + I)*\I + \/ 6 *\/ I /|| | |(6 + I)*\I - \/ 6 *\/ I /|| | |(6 + I)*\I + \/ 6 *\/ I /|| | |(6 + I)*\I - \/ 6 *\/ I /||
2*re|atan|-------------------------|| + 2*re|atan|-------------------------|| + 2*I*im|atan|-------------------------|| + 2*I*im|atan|-------------------------||
\ \ 37 // \ \ 37 // \ \ 37 // \ \ 37 //
$$2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)}$$
producto
/ / / / ___ ___\\\ / / / ___ ___\\\\ / / / / ___ ___\\\ / / / ___ ___\\\\ | | |(6 + I)*\I + \/ 6 *\/ I /|| | |(6 + I)*\I + \/ 6 *\/ I /||| | | |(6 + I)*\I - \/ 6 *\/ I /|| | |(6 + I)*\I - \/ 6 *\/ I /||| |2*re|atan|-------------------------|| + 2*I*im|atan|-------------------------|||*|2*re|atan|-------------------------|| + 2*I*im|atan|-------------------------||| \ \ \ 37 // \ \ 37 /// \ \ \ 37 // \ \ 37 ///
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)}\right)$$
=
/ / / / ___ ___\\\ / / / ___ ___\\\\ / / / / ___ ___\\\ / / / ___ ___\\\\ | | |(6 + I)*\I + \/ 6 *\/ I /|| | |(6 + I)*\I + \/ 6 *\/ I /||| | | |(6 + I)*\I - \/ 6 *\/ I /|| | |(6 + I)*\I - \/ 6 *\/ I /||| 4*|I*im|atan|-------------------------|| + re|atan|-------------------------|||*|I*im|atan|-------------------------|| + re|atan|-------------------------||| \ \ \ 37 // \ \ 37 /// \ \ \ 37 // \ \ 37 ///
$$4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(i + \sqrt{6} \sqrt{i}\right)}{37} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\left(6 + i\right) \left(- \sqrt{6} \sqrt{i} + i\right)}{37} \right)}\right)}\right)$$
4*(i*im(atan((6 + i)*(i + sqrt(6)*sqrt(i))/37)) + re(atan((6 + i)*(i + sqrt(6)*sqrt(i))/37)))*(i*im(atan((6 + i)*(i - sqrt(6)*sqrt(i))/37)) + re(atan((6 + i)*(i - sqrt(6)*sqrt(i))/37)))
Respuesta numérica
[src]
z1 = -30.8923277602996 + 1.00505253874238*i
z2 = 94.7713783832921 + 1.00505253874238*i
z3 = 101.054563690472 + 1.00505253874238*i
z4 = -100.007366139275 + 1.00505253874238*i
z5 = 12.0427718387609 - 0.311905358182436*i
z6 = -56.025068989018 + 1.00505253874238*i
z7 = 62.3082542961976 - 0.311905358182436*i
z8 = 13.0899693899575 + 1.00505253874238*i
z9 = 24.60914245312 - 0.311905358182436*i
z10 = 44.5058959258554 + 1.00505253874238*i
z11 = 50.789081233035 + 1.00505253874238*i
z12 = -93.7241808320955 + 1.00505253874238*i
z13 = 68.5914396033772 - 0.311905358182436*i
z14 = 25.6563400043166 + 1.00505253874238*i
z15 = 75.9218224617533 + 1.00505253874238*i
z16 = -19.3731546971371 - 0.311905358182436*i
z17 = -5.75958653158129 + 1.00505253874238*i
z18 = -74.8746249105567 + 1.00505253874238*i
z19 = -37.1755130674792 + 1.00505253874238*i
z20 = -57.0722665402146 - 0.311905358182436*i
z21 = -63.3554518473942 - 0.311905358182436*i
z22 = 38.2227106186758 + 1.00505253874238*i
z23 = -24.60914245312 + 1.00505253874238*i
z24 = -12.0427718387609 + 1.00505253874238*i
z25 = 30.8923277602996 - 0.311905358182436*i
z26 = -82.2050077689329 - 0.311905358182436*i
z27 = 5.75958653158129 - 0.311905358182436*i
z28 = -75.9218224617533 - 0.311905358182436*i
z29 = -18.3259571459405 + 1.00505253874238*i
z30 = -13.0899693899575 - 0.311905358182436*i
z31 = 56.025068989018 - 0.311905358182436*i
z32 = 93.7241808320955 - 0.311905358182436*i
z33 = -38.2227106186758 - 0.311905358182436*i
z34 = 57.0722665402146 + 1.00505253874238*i
z35 = 74.8746249105567 - 0.311905358182436*i
z36 = 37.1755130674792 - 0.311905358182436*i
z37 = -81.1578102177363 + 1.00505253874238*i
z38 = -43.4586983746588 + 1.00505253874238*i
z39 = 81.1578102177363 - 0.311905358182436*i
z40 = -62.3082542961976 + 1.00505253874238*i
z41 = 100.007366139275 - 0.311905358182436*i
z42 = -25.6563400043166 - 0.311905358182436*i
z43 = 88.4881930761125 + 1.00505253874238*i
z44 = 87.4409955249159 - 0.311905358182436*i
z45 = -69.6386371545737 - 0.311905358182436*i
z46 = 49.7418836818384 - 0.311905358182436*i
z47 = 18.3259571459405 - 0.311905358182436*i
z48 = -50.789081233035 - 0.311905358182436*i
z49 = 0.523598775598299 + 1.00505253874238*i
z50 = -31.9395253114962 - 0.311905358182436*i
z51 = -88.4881930761125 - 0.311905358182436*i
z52 = 6.80678408277789 + 1.00505253874238*i
z53 = -6.80678408277789 - 0.311905358182436*i
z54 = -87.4409955249159 + 1.00505253874238*i
z55 = -49.7418836818384 + 1.00505253874238*i
z56 = -68.5914396033772 + 1.00505253874238*i
z57 = -0.523598775598299 - 0.311905358182436*i
z58 = 69.6386371545737 + 1.00505253874238*i
z59 = -94.7713783832921 - 0.311905358182436*i
z60 = 31.9395253114962 + 1.00505253874238*i
z61 = -44.5058959258554 - 0.311905358182436*i
z62 = 43.4586983746588 - 0.311905358182436*i
z63 = 82.2050077689329 + 1.00505253874238*i
z64 = 63.3554518473942 + 1.00505253874238*i
z65 = 19.3731546971371 + 1.00505253874238*i
z65 = 19.3731546971371 + 1.00505253874238*i