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- La ecuación:
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Ecuación x^2-4x+5=0
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Ecuación x^2+3x+2=0
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Ecuación x^2+3x=4
-
Ecuación -x^2+5*x-6=0
- Expresar {x} en función de y en la ecuación:
- 10*x-2*y=0
- 1*x+4*y=20
- 3*x-7*y=13
- 13*x-15*y=-6
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Expresiones idénticas
- sin(z)+cos(z)=i
- seno de (z) más coseno de (z) es igual a i
- sinz+cosz=i
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Expresiones semejantes
- sin2z+5(sinz+cosz)+1=0
- sin(z)-cos(z)=i
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Expresiones con funciones
- Seno sin
- sin(6*x)=9/8
- sin2x+1=cosx+2sinx
- sin(3*x)+cos(3*x)=0
- sin2x=-1/2
- sin(x)=-(sqrt(3)/2)
- Coseno cos
- cos(x)=(-1)/sqrt(2)
- cos(2*x)+3*sin(x)-2=0
- cos(-x)=-1
- cos(2x)=1/2
- cos(4*x)=1
sin(z)+cos(z)=i la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
Respuesta rápida
[src]
/ / ___ \\ / / ___ \\
| | 1 I \/ 3 *(1 - I)|| | | 1 I \/ 3 *(1 - I)||
z1 = - 2*re|atan|- - + - + -------------|| - 2*I*im|atan|- - + - + -------------||
\ \ 2 2 2 // \ \ 2 2 2 //
$$z_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)}$$
/ / ___ \\ / / ___ \\
| |1 I \/ 3 *(1 - I)|| | |1 I \/ 3 *(1 - I)||
z2 = 2*re|atan|- - - + -------------|| + 2*I*im|atan|- - - + -------------||
\ \2 2 2 // \ \2 2 2 //
$$z_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)}$$
z2 = 2*re(atan(1/2 + sqrt(3)*(1 - i)/2 - i/2)) + 2*i*im(atan(1/2 + sqrt(3)*(1 - i)/2 - i/2))
Suma y producto de raíces
[src]
suma
/ / ___ \\ / / ___ \\ / / ___ \\ / / ___ \\
| | 1 I \/ 3 *(1 - I)|| | | 1 I \/ 3 *(1 - I)|| | |1 I \/ 3 *(1 - I)|| | |1 I \/ 3 *(1 - I)||
- 2*re|atan|- - + - + -------------|| - 2*I*im|atan|- - + - + -------------|| + 2*re|atan|- - - + -------------|| + 2*I*im|atan|- - - + -------------||
\ \ 2 2 2 // \ \ 2 2 2 // \ \2 2 2 // \ \2 2 2 //
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)}\right)$$
=
/ / ___ \\ / / ___ \\ / / ___ \\ / / ___ \\
| | 1 I \/ 3 *(1 - I)|| | |1 I \/ 3 *(1 - I)|| | | 1 I \/ 3 *(1 - I)|| | |1 I \/ 3 *(1 - I)||
- 2*re|atan|- - + - + -------------|| + 2*re|atan|- - - + -------------|| - 2*I*im|atan|- - + - + -------------|| + 2*I*im|atan|- - - + -------------||
\ \ 2 2 2 // \ \2 2 2 // \ \ 2 2 2 // \ \2 2 2 //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)}$$
producto
/ / / ___ \\ / / ___ \\\ / / / ___ \\ / / ___ \\\ | | | 1 I \/ 3 *(1 - I)|| | | 1 I \/ 3 *(1 - I)||| | | |1 I \/ 3 *(1 - I)|| | |1 I \/ 3 *(1 - I)||| |- 2*re|atan|- - + - + -------------|| - 2*I*im|atan|- - + - + -------------|||*|2*re|atan|- - - + -------------|| + 2*I*im|atan|- - - + -------------||| \ \ \ 2 2 2 // \ \ 2 2 2 /// \ \ \2 2 2 // \ \2 2 2 ///
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)}\right)$$
=
/ / / ___ \\ / / ___ \\\ / / / ___ \\ / / ___ \\\ | | |1 I \/ 3 *(1 - I)|| | |1 I \/ 3 *(1 - I)||| | | | 1 I \/ 3 *(1 - I)|| | | 1 I \/ 3 *(1 - I)||| -4*|I*im|atan|- - - + -------------|| + re|atan|- - - + -------------|||*|I*im|atan|- - + - + -------------|| + re|atan|- - + - + -------------||| \ \ \2 2 2 // \ \2 2 2 /// \ \ \ 2 2 2 // \ \ 2 2 2 ///
$$- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} + \frac{i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} \left(1 - i\right)}{2} - \frac{i}{2} \right)}\right)}\right)$$
-4*(i*im(atan(1/2 - i/2 + sqrt(3)*(1 - i)/2)) + re(atan(1/2 - i/2 + sqrt(3)*(1 - i)/2)))*(i*im(atan(-1/2 + i/2 + sqrt(3)*(1 - i)/2)) + re(atan(-1/2 + i/2 + sqrt(3)*(1 - i)/2)))
Respuesta numérica
[src]
z1 = -0.785398163397448 + 0.658478948462408*i
z2 = -44.7676953136546 + 0.658478948462408*i
z3 = 93.4623814442964 + 0.658478948462408*i
z4 = 80.8960108299372 + 0.658478948462408*i
z5 = -38.484510006475 + 0.658478948462408*i
z6 = 68.329640215578 + 0.658478948462408*i
z7 = 14.9225651045515 - 0.658478948462408*i
z8 = 2.35619449019234 - 0.658478948462408*i
z9 = -66.7588438887831 - 0.658478948462408*i
z10 = 58.9048622548086 - 0.658478948462408*i
z11 = 40.0553063332699 - 0.658478948462408*i
z12 = 55.7632696012188 + 0.658478948462408*i
z13 = -73.0420291959627 - 0.658478948462408*i
z14 = 99.7455667514759 + 0.658478948462408*i
z15 = 52.621676947629 - 0.658478948462408*i
z16 = 71.4712328691678 - 0.658478948462408*i
z17 = -60.4756585816035 - 0.658478948462408*i
z18 = 46.3384916404494 - 0.658478948462408*i
z19 = 43.1968989868597 + 0.658478948462408*i
z20 = 77.7544181763474 - 0.658478948462408*i
z21 = -13.3517687777566 + 0.658478948462408*i
z22 = -19.6349540849362 + 0.658478948462408*i
z23 = -82.4668071567321 + 0.658478948462408*i
z24 = -54.1924732744239 - 0.658478948462408*i
z25 = -98.174770424681 - 0.658478948462408*i
z26 = 33.7721210260903 - 0.658478948462408*i
z27 = 21.2057504117311 - 0.658478948462408*i
z28 = 8.63937979737193 - 0.658478948462408*i
z29 = 24.3473430653209 + 0.658478948462408*i
z30 = -22.776546738526 - 0.658478948462408*i
z31 = 27.4889357189107 - 0.658478948462408*i
z32 = -63.6172512351933 + 0.658478948462408*i
z33 = 62.0464549083984 + 0.658478948462408*i
z34 = -57.3340659280137 + 0.658478948462408*i
z35 = -16.4933614313464 - 0.658478948462408*i
z36 = -79.3252145031423 - 0.658478948462408*i
z37 = -85.6083998103219 - 0.658478948462408*i
z38 = 36.9137136796801 + 0.658478948462408*i
z39 = -32.2013246992954 + 0.658478948462408*i
z40 = -10.2101761241668 - 0.658478948462408*i
z41 = 18.0641577581413 + 0.658478948462408*i
z42 = -91.8915851175014 - 0.658478948462408*i
z43 = 90.3207887907066 - 0.658478948462408*i
z44 = 30.6305283725005 + 0.658478948462408*i
z45 = 96.6039740978861 - 0.658478948462408*i
z46 = -29.0597320457056 - 0.658478948462408*i
z47 = -95.0331777710912 + 0.658478948462408*i
z48 = 65.1880475619882 - 0.658478948462408*i
z49 = -47.9092879672443 - 0.658478948462408*i
z50 = 74.6128255227576 + 0.658478948462408*i
z51 = -41.6261026600648 - 0.658478948462408*i
z52 = -69.9004365423729 + 0.658478948462408*i
z53 = 84.037603483527 - 0.658478948462408*i
z54 = -88.7499924639117 + 0.658478948462408*i
z55 = -76.1836218495525 + 0.658478948462408*i
z56 = -35.3429173528852 - 0.658478948462408*i
z57 = -51.0508806208341 + 0.658478948462408*i
z58 = -3.92699081698724 - 0.658478948462408*i
z59 = 11.7809724509617 + 0.658478948462408*i
z60 = 49.4800842940392 + 0.658478948462408*i
z61 = 87.1791961371168 + 0.658478948462408*i
z62 = -25.9181393921158 + 0.658478948462408*i
z63 = -7.06858347057703 + 0.658478948462408*i
z64 = 5.49778714378214 + 0.658478948462408*i
z64 = 5.49778714378214 + 0.658478948462408*i