Question

Ajuda, nesta também!!!

Answer 1

Observe:

$i=\sqrt{-1}\\ \\i^2=(\sqrt{-1})^2=-1\\ \\i^5=i^2\cdot i^2\cdot i=(-1)\cdot(-1)\cdot i=1\cdot i=i$

$(1-i)^{10}+(1+i)^{10}=\\ \\=[(1-i)^2]^5+[(1+i)^2]^5=\\ \\=[1-2i+i^2]^5+[1+2i+i^2]^5=\\ \\=[1-2i-1]^5+[1+2i-1]^5=\\ \\=[-2i]^5+[2i]^5=\\ \\=-32i^5+32i^5=\\ \\=-32i+32i=\\ \\=0$