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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación x(x^2+2x+1)=6(x+1)
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Ecuación 4x+1=-3x+15
- Ecuación (3x−36)⋅(x+8)=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
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Expresiones idénticas
- sin(z)-cos(z)=i
- seno de (z) menos coseno de (z) es igual a i
- sinz-cosz=i
-
Expresiones semejantes
- sin(z)+cos(z)=i
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Expresiones con funciones
- Seno sin
- sin(x)=pi
- sin(4*x)=0
- sin(x)^2=1
- sin(x)=(1/2)
- sin(x)+sin(2*x)+sin(3*x)=0
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
sin(z)-cos(z)=i la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
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 //
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)}\right)$$
=
/ / ___ \\ / / ___ \\ / / ___ \\ / / ___ \\
| |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 //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)}$$
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 ///
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)}\right)$$
=
/ / / ___ \\ / / ___ \\\ / / / ___ \\ / / ___ \\\ | | |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 ///
$$4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} \left(1 + i\right)}{2} + \frac{i}{2} \right)}\right)}\right)$$
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 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 //
$$z_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{i}{2} + \frac{\sqrt{3} \left(1 + i\right)}{2} \right)}\right)}$$
/ / ___ \\ / / ___ \\
| |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))
Respuesta numérica
[src]
z1 = -5.49778714378214 + 0.658478948462408*i
z2 = -65.1880475619882 - 0.658478948462408*i
z3 = 0.785398163397448 + 0.658478948462408*i
z4 = -46.3384916404494 - 0.658478948462408*i
z5 = -30.6305283725005 + 0.658478948462408*i
z6 = 101.316363078271 + 0.658478948462408*i
z7 = -18.0641577581413 + 0.658478948462408*i
z8 = 32.2013246992954 + 0.658478948462408*i
z9 = -43.1968989868597 + 0.658478948462408*i
z10 = -77.7544181763474 - 0.658478948462408*i
z11 = -49.4800842940392 + 0.658478948462408*i
z12 = 57.3340659280137 + 0.658478948462408*i
z13 = -55.7632696012188 + 0.658478948462408*i
z14 = -14.9225651045515 - 0.658478948462408*i
z15 = 88.7499924639117 + 0.658478948462408*i
z16 = 82.4668071567321 + 0.658478948462408*i
z17 = 13.3517687777566 + 0.658478948462408*i
z18 = -96.6039740978861 - 0.658478948462408*i
z19 = -2.35619449019234 - 0.658478948462408*i
z20 = -93.4623814442964 + 0.658478948462408*i
z21 = -99.7455667514759 + 0.658478948462408*i
z22 = 76.1836218495525 + 0.658478948462408*i
z23 = -52.621676947629 - 0.658478948462408*i
z24 = -36.9137136796801 + 0.658478948462408*i
z25 = -58.9048622548086 - 0.658478948462408*i
z26 = 98.174770424681 - 0.658478948462408*i
z27 = -87.1791961371168 + 0.658478948462408*i
z28 = 22.776546738526 - 0.658478948462408*i
z29 = 66.7588438887831 - 0.658478948462408*i
z30 = -68.329640215578 + 0.658478948462408*i
z31 = 63.6172512351933 + 0.658478948462408*i
z32 = 25.9181393921158 + 0.658478948462408*i
z33 = 7.06858347057703 + 0.658478948462408*i
z34 = 3.92699081698724 - 0.658478948462408*i
z35 = -21.2057504117311 - 0.658478948462408*i
z36 = 95.0331777710912 + 0.658478948462408*i
z37 = 47.9092879672443 - 0.658478948462408*i
z38 = -24.3473430653209 + 0.658478948462408*i
z39 = -80.8960108299372 + 0.658478948462408*i
z40 = -40.0553063332699 - 0.658478948462408*i
z41 = -84.037603483527 - 0.658478948462408*i
z42 = -11.7809724509617 + 0.658478948462408*i
z43 = 29.0597320457056 - 0.658478948462408*i
z44 = 10.2101761241668 - 0.658478948462408*i
z45 = 38.484510006475 + 0.658478948462408*i
z46 = -33.7721210260903 - 0.658478948462408*i
z47 = 60.4756585816035 - 0.658478948462408*i
z48 = -27.4889357189107 - 0.658478948462408*i
z49 = 54.1924732744239 - 0.658478948462408*i
z50 = 19.6349540849362 + 0.658478948462408*i
z51 = 69.9004365423729 + 0.658478948462408*i
z52 = -8.63937979737193 - 0.658478948462408*i
z53 = 44.7676953136546 + 0.658478948462408*i
z54 = 85.6083998103219 - 0.658478948462408*i
z55 = -62.0464549083984 + 0.658478948462408*i
z56 = 16.4933614313464 - 0.658478948462408*i
z57 = -74.6128255227576 + 0.658478948462408*i
z58 = -71.4712328691678 - 0.658478948462408*i
z59 = 73.0420291959627 - 0.658478948462408*i
z60 = 35.3429173528852 - 0.658478948462408*i
z61 = -90.3207887907066 - 0.658478948462408*i
z62 = 91.8915851175014 - 0.658478948462408*i
z63 = 51.0508806208341 + 0.658478948462408*i
z64 = 79.3252145031423 - 0.658478948462408*i
z65 = 41.6261026600648 - 0.658478948462408*i
z65 = 41.6261026600648 - 0.658478948462408*i