Question

Express (1-2i)^-3 in a +ib

Answer 1

$( {1 - 2i)}^{2} \\ = {1}^{3} - {(2i)}^{3} - 3 {(1)}^{2} ( - 2i) + 3(1) {( 2i)}^{2} \\ = 1 - ( - 8i) + 6i + 3( - 4) \\ = 1 + 8i + 6i - 12 \\ = - 11 + 14i$