Question

01) Sendo i a unidade imaginária, o valor de é:

Answer 1

$(\frac{1+i}{1-i})^4=\frac{(1+i)^4}{(1-i)^4}=\frac{(1+i)^2(1+i)^2}{(1-i)^2(1-i)^2}=\\\\ =\frac{(1+2i+i^2)(1+2i+i^2)}{(1-2i+i^2)(1-2i+i^2)}=\\\\ =\frac{(1+2i-1)(1+2i-1)}{(1-2i-1)(1-2i-1)}=\\\\ =\frac{(2i)(2i)}{(-2i)(-2i)}=\frac{4i^2}{4i^2}=1$