Question

efetue a seguinte questão (2+2i)⁴

Answer 1

(2+2i)⁴ = 16 + 64i + 96i² + 64i³ + 16i⁴

= 16 + 64i - 96 - 64i + 16

= 16 - 96 + 16

= -64

Answer 2

Olá!

Podemos, também, resolver do seguinte modo:

$\\ \displaystyle \mathsf{(2 + 2i)^4 =} \\\\ \mathsf{\left [ 2 \cdot (1 + i) \right ]^4 =} \\\\ \mathsf{2^4 \cdot (1 + i)^4 =} \\\\ \mathsf{16 \cdot (1 + i)^2 \cdot (1 + i)^2 =} \\\\ \mathsf{16 \cdot (1 + 2i + i^2) \cdot (1 + 2i + i^2) =} \\\\ \mathsf{16 \cdot (1 + 2i - 1) \cdot (1 + 2i - 1) =} \\\\ \mathsf{16 \cdot (2i) \cdot (2i) =} \\\\ \mathsf{16 \cdot 4i^2 =} \\\\ \mathsf{64 \cdot (- 1) =} \\\\ \boxed{\mathsf{- 64}}$