Question

me ajudem.

calcule (1+ i)¹0

Answer 1

$(1+i)^{10}=\left[(1+i)^{2}\right]^{5}$

Vamos achar (1+i)²:

$(1+i)^{2}=1^{2}+2.1.i+i^{2}\\(1+i)^{2}=1+2i-1\\(1+i)^{2}=2i$

Substituindo:

$(1+i)^{10}=\left[(1+i)^{2}\right]^{5}\\(1+i)^{10}=\left[2i\right]^{5}\\(1+i)^{10}=2^{5}i^{5}\\(1+i)^{10}=32i^{1}\\\\\boxed{\boxed{(1+i)^{10}=32i}}$