Question

$(1+i{)}^n$ find min +ve integer n such that it represents (i) an integer
(ii) a +ve integer

Answer 1

$(1+i{)}^n=\{(1+i{)}^2{\}}^{\frac{n}{2}}=(2i{)}^{\frac{n}{2}}$

(i) ${\left(\frac{n}{2}\right)}_{min}=2\Rightarrow n=4$

(ii) ${\left(\frac{n}{2}\right)}_{min}=4\Rightarrow n=8$