Question

Dado z=2+2i, qual o valor de z^12?

Answer 1

Explicação passo-a-passo:

$z^2=(2+2i)^2$

$z^2=4+8i+4i^2$

$z^2=4+8i-4$

$z^2=8i$

Assim:

$z^{12}=(z^2)^6$

$z^{12}=(8i)^6$

$z^{12}=8^6\cdot i^6$

$z^{12}=(2^3)^{6}\cdot(i^2)^3$

$z^{12}=2^{18}\cdot(-1)^3$

$z^{12}=-2^{18}$

$z^{12}=-262144$