Question

Realiza la siguinte division de numero complejo 1. (5+6i)/(3+7i) :
2.(4+3i)/(2+i):
3.(12+4i)/(1+3i):
4.(6-2i)/(5+2i):
5.(8+41)/(3-4i):

por favor lo nesecito para hoy eso

El mejor que responda se lleva 15 puntos ​

Answer 1

Explicación paso a paso:

Aplicas la formula para los 5 fracciones

$\frac{a+bi}{c+di}\:=\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}$

1)

$\frac{5+6i}{3+7i}\\\\\frac{\left(5\cdot \:3+6\cdot \:7\right)+\left(6\cdot \:3-5\cdot \:7\right)i}{3^2+7^2}\\\\\frac{57}{58}-\frac{17}{58}i$

2)

$\frac{4+3i}{2+i}\\\\\frac{\left(4\cdot \:2+3\cdot \:1\right)+\left(3\cdot \:2-4\cdot \:1\right)i}{2^2+1^2}\\\\\frac{11}{5}+\frac{2}{5}i$

3)

$\frac{12+4i}{1+3i}\\\\\frac{\left(12\cdot \:1+4\cdot \:3\right)+\left(4\cdot \:1-12\cdot \:3\right)i}{1^2+3^2}\\\\\frac{12}{5}-\frac{16}{5}i$

4)

$\frac{6-2i}{5+2i}\\\\\frac{\left(6\cdot \:5+\left(-2\right)\cdot \:2\right)+\left(-2\cdot \:5-6\cdot \:2\right)i}{5^2+2^2}\\\\\frac{26}{29}-\frac{22}{29}i$

5)

$\frac{8+4i}{3-4i}\\\\\frac{\left(8\cdot \:3+4\left(-4\right)\right)+\left(4\cdot \:3-8\left(-4\right)\right)i}{3^2+\left(-4\right)^2}\\\\\frac{8}{25}+\frac{44}{25}i$