Question

Perform the indicated operations.
$(1+i{)}^{20}.$

Answer 1

$1+i=\sqrt{2}{e}^{i\pi /4}$

${(1+i)}^{20}={\left(\sqrt{2}{e}^{i\pi /4}\right)}^{20}=1024\times e^{5i\pi }$

$=-1024$