Question

locate the points representing the complex number $z$ for which
$|z-i|=1$ and $argz=\pi /2$

Answer 1

Here the equation $|z-i|=1$ represents all points $z$ on the boundary of circle whose center is $i$ and radius 1. And the equation age $z=\pi /2$ represents all point on the positive side of $y-$axis excluding the origin. These two regions have only one common point $A$ whose co-ordination are $(0,2).$
Hence the two equation $|z-i|=1$ and $\arg z=\pi /2$ represent only one point $A(0,2).$