Question

Prove que prove que (1+i)² = 2i e coloque na forma algébrica o número: z = [(1 +i)^(80) - (1 + i)^(82)]/i^96

Answer 1

(1 + i)² = 1 +2.1.i + i² = 1 + 2 - 1 = 2i

(1+ i)⁸⁰ = [(1+i)²]⁴⁰ = (2i)⁴⁰ = 2⁴⁰.i⁴⁰ = 2⁴⁰.i⁰ = 2⁴⁰.1 = 2⁴⁰

(1 + i)⁸² = [(1 + 1)²]⁴¹ = (2i)⁴¹ = 2⁴¹.i⁴¹ = 2⁴¹.i¹ = 2⁴¹i

i⁹⁶ = i⁰ = 1

(2⁴⁰ - 2⁴¹i)/1 = 2⁴⁰ - 2⁴¹i = 2⁴⁰(1 - 2i)