Question

Números Complexos
Z1=$\frac{(1-i)^{2}+9i^3^4 }{1+2i}$

Answer 1

$Z = \frac{(1-i)^2+9i^3^4}{1+2i}\\\\ i^3^4 = i^2 = -1\\\\ Z = \frac{1-2i+i^2+9i^2}{1+2i}\\\\ Z=\frac{1-2i+10i^2}{1+2i}\\\\ Z = \frac{1-10-2i}{1+2i}$

$Z=\frac{-9-2i}{1+2i}\ \frac{1-2i}{1-2i}\ \frac{-9-18i-2i-4i^2}{1-2i+2i-4i^2}\ \frac{-5-20i}{5}\\\\ Z=\frac{-5-20i}{5}\\\\ \boxed{Z=-1-4i}$