Question

What is (1-i)^3 Please explain how you got that

Answer 1

$\bf (1-i)^3\implies ~\hfill \begin{array}{cccccccl} 1^3&+&3(1)^2(-i)^1&+&3(1)^1(i)^2&+&(-i)^3\\\\ 1&+&(-3i)&+&(3i^2)&+&(-i^3)\\\\ 1&-&3i&+&3i^2&-&i^3 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{let's recall that}}{i^2=-1\qquad \qquad i^3=-i} \\\\[-0.35em] ~\dotfill\\\\ 1-3i+3(-1)-(-i)\implies 1-3i-3+i\implies -2-2i$