Question

Provar que (1-i)^2 = -2i e calcular (1 - i)^96 + (1-i)^97

Answer 1

Bom dia Belinha

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

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

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

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

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