Question

Aratati ca (1+i)la puterea a 4=-4

Answer 1

${(1 + i)}^{4} = \\ \\ {(1 + i)}^{2 + 2} = \\ \\ {(1 + i)}^{2} \times {(1 + i)}^{2} = \\ \\ {1}^{2} + 2 \times 1i + {i}^{2} \times {1}^{2} + 2 \times 1i + {i}^{2} = \\ \\ (1 + 2i + {i}^{2}) \times (1 + 2i + {i}^{2}) = \\ \\ (1 + 2i - 1) \times (1 + 2i - 1) = \\ \\ 2i \times 2i = \\ \\ {4i}^{1} \times {i}^{1} = \\ \\ {4i}^{1 + 1} = \\ \\ {4i}^{2} = \\ \\ 4 \times ( - 1) = \\ \\ - (4 \times 1) = \\ \\ - 4$

Answer 2

(1+i)⁴ = [(1+i)²]² = (1-2i+i²)² =

= (1-2i-1)² = (-2i)² = (2i)² = 2²•i² = -4