Question

help with this blank question

Answer 1

$i=\sqrt{-1}\to i^2=-1\\\\i^{15}=i^{1+14}=i^1\cdot i^{14}=i\cdot i^{2\cdot7}=i\cdot (i^2)^7=i\cdot(-1)^7=i\cdot(-1)=-i$

$\text{Used:}\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{n\cdot m}$