Question

Sendo o a unidade imaginária , (1-i)^-2

Answer 1

$\mathrm{(1-i)^{-2}=\dfrac{1}{(1-i)^2}=\dfrac{1}{1-2i+(-i)^2}=}\\\\ \mathrm{=\dfrac{1}{1-2i-1}=\dfrac{1}{-2i}=\dfrac{1}{-2i}\times\dfrac{i}{i}=\dfrac{i}{-2i^2}=}\\\\ \mathrm {=\dfrac{i}{-2(-1)}=\boxed{\mathbf{\dfrac{i}{2}}}}$