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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
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Expresiones semejantes
- cos(z-i)=-3/4*i
- cos(z+i)=+3/4*i
- 3*cos(z)+i*sin(z)=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
cos(z+i)=-3/4*i la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(z + i \right)} = - \frac{3 i}{4}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$z + i = \pi n + \operatorname{acos}{\left(- \frac{3 i}{4} \right)}$$
$$z + i = \pi n - \pi + \operatorname{acos}{\left(- \frac{3 i}{4} \right)}$$
O
$$z + i = \pi n + \frac{\pi}{2} + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
$$z + i = \pi n - \frac{\pi}{2} + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
, donde n es cualquier número entero
Transportemos
$$i$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$z = \pi n + \frac{\pi}{2} - i + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
$$z = \pi n - \frac{\pi}{2} - i + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
$$\cos{\left(z + i \right)} = - \frac{3 i}{4}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$z + i = \pi n + \operatorname{acos}{\left(- \frac{3 i}{4} \right)}$$
$$z + i = \pi n - \pi + \operatorname{acos}{\left(- \frac{3 i}{4} \right)}$$
O
$$z + i = \pi n + \frac{\pi}{2} + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
$$z + i = \pi n - \frac{\pi}{2} + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
, donde n es cualquier número entero
Transportemos
$$i$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$z = \pi n + \frac{\pi}{2} - i + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
$$z = \pi n - \frac{\pi}{2} - i + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
Gráfica
Suma y producto de raíces
[src]
suma
pi 3*pi -- + I*(-1 + asinh(3/4)) + ---- + I*(-1 - asinh(3/4)) 2 2
$$\left(\frac{3 \pi}{2} + i \left(-1 - \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)\right) + \left(\frac{\pi}{2} + i \left(-1 + \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)\right)$$
=
2*pi + I*(-1 - asinh(3/4)) + I*(-1 + asinh(3/4))
$$2 \pi + i \left(-1 - \operatorname{asinh}{\left(\frac{3}{4} \right)}\right) + i \left(-1 + \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)$$
producto
/pi \ /3*pi \ |-- + I*(-1 + asinh(3/4))|*|---- + I*(-1 - asinh(3/4))| \2 / \ 2 /
$$\left(\frac{\pi}{2} + i \left(-1 + \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)\right) \left(\frac{3 \pi}{2} + i \left(-1 - \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)\right)$$
=
(pi + 2*I*(-1 + asinh(3/4)))*(3*pi - 2*I*(1 + asinh(3/4)))
----------------------------------------------------------
4
$$\frac{\left(\pi + 2 i \left(-1 + \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)\right) \left(3 \pi - 2 i \left(\operatorname{asinh}{\left(\frac{3}{4} \right)} + 1\right)\right)}{4}$$
(pi + 2*i*(-1 + asinh(3/4)))*(3*pi - 2*i*(1 + asinh(3/4)))/4
Respuesta rápida
[src]
pi
z1 = -- + I*(-1 + asinh(3/4))
2
$$z_{1} = \frac{\pi}{2} + i \left(-1 + \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)$$
3*pi
z2 = ---- + I*(-1 - asinh(3/4))
2
$$z_{2} = \frac{3 \pi}{2} + i \left(-1 - \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)$$
z2 = 3*pi/2 + i*(-1 - asinh(3/4))
Respuesta numérica
[src]
z1 = 39.2699081698724 - 0.306852819440055*i
z2 = 83.2522053201295 - 0.306852819440055*i
z3 = -26.7035375555132 - 1.69314718055995*i
z4 = 73.8274273593601 - 1.69314718055995*i
z5 = 23.5619449019235 - 1.69314718055995*i
z6 = 92.6769832808989 - 1.69314718055995*i
z7 = 86.3937979737193 - 1.69314718055995*i
z8 = 54.9778714378214 - 1.69314718055995*i
z9 = -51.8362787842316 - 1.69314718055995*i
z10 = 98.9601685880785 - 1.69314718055995*i
z11 = -29.845130209103 - 0.306852819440055*i
z12 = -45.553093477052 - 1.69314718055995*i
z13 = 4.71238898038469 - 1.69314718055995*i
z14 = 7.85398163397448 - 0.306852819440055*i
z15 = -20.4203522483337 - 1.69314718055995*i
z16 = 36.1283155162826 - 1.69314718055995*i
z17 = 42.4115008234622 - 1.69314718055995*i
z18 = -7.85398163397448 - 1.69314718055995*i
z19 = -70.6858347057703 - 1.69314718055995*i
z20 = 20.4203522483337 - 0.306852819440055*i
z21 = 76.9690200129499 - 0.306852819440055*i
z22 = 26.7035375555132 - 0.306852819440055*i
z23 = -83.2522053201295 - 1.69314718055995*i
z24 = -4.71238898038469 - 0.306852819440055*i
z25 = -32.9867228626928 - 1.69314718055995*i
z26 = -64.4026493985908 - 1.69314718055995*i
z27 = -58.1194640914112 - 1.69314718055995*i
z28 = 51.8362787842316 - 0.306852819440055*i
z29 = -76.9690200129499 - 1.69314718055995*i
z30 = -95.8185759344887 - 1.69314718055995*i
z31 = -89.5353906273091 - 1.69314718055995*i
z32 = 45.553093477052 - 0.306852819440055*i
z33 = -1.5707963267949 - 1.69314718055995*i
z34 = -86.3937979737193 - 0.306852819440055*i
z35 = -92.6769832808989 - 0.306852819440055*i
z36 = -14.1371669411541 - 1.69314718055995*i
z37 = 48.6946861306418 - 1.69314718055995*i
z38 = 80.1106126665397 - 1.69314718055995*i
z39 = 67.5442420521806 - 1.69314718055995*i
z40 = -10.9955742875643 - 0.306852819440055*i
z41 = -17.2787595947439 - 0.306852819440055*i
z42 = -42.4115008234622 - 0.306852819440055*i
z43 = -61.261056745001 - 0.306852819440055*i
z44 = 1.5707963267949 - 0.306852819440055*i
z45 = 64.4026493985908 - 0.306852819440055*i
z46 = 89.5353906273091 - 0.306852819440055*i
z47 = 17.2787595947439 - 1.69314718055995*i
z48 = 95.8185759344887 - 0.306852819440055*i
z49 = 14.1371669411541 - 0.306852819440055*i
z50 = -23.5619449019235 - 0.306852819440055*i
z51 = -98.9601685880785 - 0.306852819440055*i
z52 = -67.5442420521806 - 0.306852819440055*i
z53 = -39.2699081698724 - 1.69314718055995*i
z54 = -36.1283155162826 - 0.306852819440055*i
z55 = -54.9778714378214 - 0.306852819440055*i
z56 = 29.845130209103 - 1.69314718055995*i
z57 = 10.9955742875643 - 1.69314718055995*i
z58 = -73.8274273593601 - 0.306852819440055*i
z59 = -48.6946861306418 - 0.306852819440055*i
z60 = -80.1106126665397 - 0.306852819440055*i
z61 = 58.1194640914112 - 0.306852819440055*i
z62 = 61.261056745001 - 1.69314718055995*i
z63 = 32.9867228626928 - 0.306852819440055*i
z64 = 70.6858347057703 - 0.306852819440055*i
z64 = 70.6858347057703 - 0.306852819440055*i