Question

Calculati $(1-i)^{2014}$

Answer 1

z=1-i
Scrii   numarul   z  sub  forma  trigonometrica
lzl=√[(1)²+(-1)²]=√y
cosα=1/√2=√2/2
sinα=-1/√2=-√2  Din  cele   2   egalitati   rezulta  ca   α e  situat  in  cadranul   4
α=π/4+3π/2=7π/4
z=cos 7π/4+isin7π/4
Aplici   formula  lui  Moivre
z=cos 2014*π/4+isin2014*π/4=cos1007π/2+isin1007/π/2