Answer
x=$\frac{\pi}{2}$
and
y=$\frac{\pi}{4}$ or y=$\frac{5 \pi}{4}$
Work Step by Step
So,
(Sin^{2} x+1 ) + i tan y = 2sin x+i
Now By comparing the like terms on both sides, we will get
$Sin^{2} x +1 = 2 sin x, tan y=1$
=> $Sin^{2} x - 2 Sin x +1 = 0, tan y =1$
=>$( sin x - 1)^{y}=0 , tan y =1$
=> sin x =1, tan y=1
=> x=$\frac{\pi}{2}$
and
y=$\frac{\pi}{4} $or
$ y=\frac{5 \pi}{4}$