Question

Dados os números complexos Z1=3+2i e Z2=2-5i , qual é o valor de |z1.z2| ao quadrado ?

Answer 1

$\begin{matrix}|Z_1\cdot Z_2|^2&=&|(3+2i)\cdot(2-5i)|^2\\\\&=&|6-15i+4i-10i^2|^2\\\\&=&|6-11i-10(-1)|^2\\\\&=&|6-11i+10|^2\\\\&=&|16-11i|^2\\\\&=&\left(\sqrt{16^2+(-11)^2}\right)^2\\\\&=&16^2+(-11)^2\\\\&=&256+121\\\\|Z_1\cdot Z_2|^2&=&377\end{matrix}$