Question

efetue (1+i)^5 . (1-i)^5

Answer 1

Olá Bruna!

Note que os expoentes são iguais, então fazemos:

$\\ \displaystyle \mathsf{(1 + i)^5 \cdot (1 - i)^5 =} \\\\ \mathsf{\left [ (1 + i) \cdot (1 - i) \right ]^5 =} \\\\ \mathsf{(1 - i^2)^5 =} \\\\ \mathsf{\left [ 1 - (- 1) \right ]^5 =} \\\\ \mathsf{(1 + 1)^5 =} \\\\ \mathsf{2^5 =} \\\\ \boxed{\mathsf{32}}$

Lembre-se que:

$\mathbf{a^n \cdot b^n = (a \cdot b)^n = (ab)^n}$