Question

Prove que (1-i)^2=-2i e calcule (1-i)^96+(1-i)97.

Answer 1

Boa tarde Giovanig

a)

(1 - i)² = 1 - 2i + i² = 1 - 2i - 1 = -2i

b)

(1 - i)^96 = ((1 - i)²)^48 = (-2i)^48 = 2^48 

(1 - i)^97 = (1 - i)^96*(1 - i) = 2^48*(1 - i)

(1 - i)^96 + (1 - i)^97 = 2^48 + 2^48 - 2^48i = 2^49 - 2^48i