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ctgz=(-12-i)/5 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
         -12 - I
cot(z) = -------
            5   
$$\cot{\left(z \right)} = \frac{-12 - i}{5}$$
Solución detallada
Tenemos la ecuación
$$\cot{\left(z \right)} = \frac{-12 - i}{5}$$
cambiamos
$$\cot{\left(z \right)} + \frac{12}{5} + \frac{i}{5} = 0$$
$$\cot{\left(z \right)} - \frac{-12 - i}{5} = 0$$
Sustituimos
$$w = \cot{\left(z \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
w - -12/5+i/5 = 0

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
12/5 + w + i/5 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w + \frac{i}{5} = - \frac{12}{5}$$
Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
$$\frac{\left(-1\right) i}{5} + w + \frac{i}{5} = \frac{\left(-1\right) i}{5} - \frac{12}{5}$$
Dividamos ambos miembros de la ecuación en (w - i/5 + i/5)/w
w = -12/5 - i/5 / ((w - i/5 + i/5)/w)

Obtenemos la respuesta: w = -12/5 - i/5
hacemos cambio inverso
$$\cot{\left(z \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida [src]
         /    /12   I\\       /    /12   I\\
z1 = - re|acot|-- + -|| - I*im|acot|-- + -||
         \    \5    5//       \    \5    5//
$$z_{1} = - \operatorname{re}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)}$$
z1 = -re(acot(12/5 + i/5)) - i*im(acot(12/5 + i/5))
Suma y producto de raíces [src]
suma
    /    /12   I\\       /    /12   I\\
- re|acot|-- + -|| - I*im|acot|-- + -||
    \    \5    5//       \    \5    5//
$$- \operatorname{re}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)}$$
=
    /    /12   I\\       /    /12   I\\
- re|acot|-- + -|| - I*im|acot|-- + -||
    \    \5    5//       \    \5    5//
$$- \operatorname{re}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)}$$
producto
    /    /12   I\\       /    /12   I\\
- re|acot|-- + -|| - I*im|acot|-- + -||
    \    \5    5//       \    \5    5//
$$- \operatorname{re}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)}$$
=
    /    /12   I\\       /    /12   I\\
- re|acot|-- + -|| - I*im|acot|-- + -||
    \    \5    5//       \    \5    5//
$$- \operatorname{re}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acot}{\left(\frac{12}{5} + \frac{i}{5} \right)}\right)}$$
-re(acot(12/5 + i/5)) - i*im(acot(12/5 + i/5))
Respuesta numérica [src]
z1 = -91.4988860358027 + 0.0294457589140959*i
z2 = 40.4480054149686 + 0.0294457589140959*i
z3 = 93.8550805259951 + 0.0294457589140959*i
z4 = 56.1559686829176 + 0.0294457589140959*i
z5 = -47.5165888855456 + 0.0294457589140959*i
z6 = 34.164820107789 + 0.0294457589140959*i
z7 = 62.4391539900971 + 0.0294457589140959*i
z8 = 71.8639319508665 + 0.0294457589140959*i
z9 = -3.53429173528852 + 0.0294457589140959*i
z10 = 27.8816348006094 + 0.0294457589140959*i
z11 = 78.1471172580461 + 0.0294457589140959*i
z12 = 84.4303025652257 + 0.0294457589140959*i
z13 = 18.45685683984 + 0.0294457589140959*i
z14 = -53.7997741927252 + 0.0294457589140959*i
z15 = -60.0829594999048 + 0.0294457589140959*i
z16 = -31.8086256175967 + 0.0294457589140959*i
z17 = -82.0741080750334 + 0.0294457589140959*i
z18 = 49.872783375738 + 0.0294457589140959*i
z19 = -69.5077374606742 + 0.0294457589140959*i
z20 = -19.2422550032375 + 0.0294457589140959*i
z21 = 12.1736715326604 + 0.0294457589140959*i
z22 = 100.138265833175 + 0.0294457589140959*i
z23 = -38.0918109247762 + 0.0294457589140959*i
z24 = -9.8174770424681 + 0.0294457589140959*i
z25 = -16.1006623496477 + 0.0294457589140959*i
z26 = -75.7909227678538 + 0.0294457589140959*i
z27 = 5.89048622548086 + 0.0294457589140959*i
z28 = -97.7820713429823 + 0.0294457589140959*i
z29 = -25.5254403104171 + 0.0294457589140959*i
z29 = -25.5254403104171 + 0.0294457589140959*i