Let $z$ represent a complex number. Then the curve, on which roots of the equation $(z-i)^n = \sqrt{21} + 2i$ lies on a circle with center at ? (where $i = \sqrt{-1}$)
My attempt :
$z-i$ should be $nth$ roots of the complex number $\sqrt{21} + 2i$. Hence, $$ z-i = (\sqrt{21} + 2i)^{\frac{1}{n}} $$ $$ z-i = 5\bigg(\frac{\sqrt{21}}{5} + \frac{2i}{5})^{\frac1n}\bigg)$$ Now this is in polar form, but what do I do next?
Hint: Take the norm of both sides of the defining equation.