Question

Números complexos
O módulo De $\frac{(1+i) ^{2} }{3+4i}$ é:
a) $\frac{3}{25}$
b)$\frac{4}{25}$
c)$\frac{3}{5}$
d)$\frac{4}{5}$
e)$\frac{2}{5}$

Answer 1

$\frac{(1+i)^2}{3+4i}=\frac{1+2i-1}{3+4i}=\frac{2i}{3+4i}.\frac{3-4i}{3-4i}=\frac{6i+8}{9+16}=\frac{8+6i}{25} \\ \\ \boxed{\rho=\sqrt{\frac{64}{625}+\frac{36}{625}}=\sqrt{\frac{100}{625}}=\frac{2}{5}}$