Mathematics - Complex Number Question with Solution | TestHub

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

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

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

$=\frac{{\left(2\right)}^{\frac{n+2}{2}}{i}^{\frac{n+2}{2}}}{(-1{)}^{\frac{n-2}{2}}}$
Clearly $n$ must be even $n=2,4$ rejected. 

So the least positive integer possible is $n=6$