Question

Evaluate (1 - i + i²)⁻¹⁵

Answer 1

answer.................

Answer 2

As we know that

${i}^{2} = - 1$
So

${(1 - i + {i}^{2} })^{ - 15} \\ \\ = {(1 - i - 1})^{ - 15} \\ \\ = {(0 - i })^{ - 15} \\ \\ = {( - i)}^{ - 15} \\ \\ = \frac{ - 1}{ { i}^{15} } \\ \\ = \frac{ - 1}{ { i}^{4 \times 3 + 3} } \\ \\ = \frac{ - 1}{ { i}^{4 \times 3 } {i}^{3} } \\ \\ = \frac{ - 1}{ {i}^{3} } \\ \\ = \frac{ - 1}{ {i}^{2} i} \\ \\ = \frac{ - 1 }{ - i} \\ \\ = \frac{1}{i} \times \frac{i}{i} \\ \\ = \frac{i}{ {i}^{2} } \\ \\ so \\ \\ {(1 - i + {i}^{2} })^{ - 15} = - i$
Hope it helps you.