Question

Cât este (1+i) la putera 4?
Şi (1-i) la puterea 4?

Answer 1

Despre numarul imaginar i stii ca
$i^{2}=-1$
Asadar
$(1+i)^{4}=((1+i)^{2})^{2}=(1+i^{2}+2i)^{2}=(1-1+2i)^{2}=(2i)^{2}=4*i^{2}=-4$
Similar
$(1-i)^{4}=((1-i)^{2})^{2}=(1+i^{2}-2i)^{2}=(1-1-2i)^{2}=(-2i)^{2}=4*i^{2}=-4$

Answer 2

(1+i)⁴=[(1+i)²]²=(1+2i+i²)²=(1+2i-1)²=4i²=-4
(1-i)⁴=[(1-i)²]²=(1-2i+i²)²=(1-2i-1)²=4i²=-4