The complex number $z$ has a modulus $r$ and principal argument $\theta $ where \(0

Question

The complex number $z$ has a modulus $r$ and principal argument $\theta $ where $0<\theta <\frac{\pi }{2}$. Find, in terms of $r$ and $\theta $, the modulus and argument of ${{z}^{-1}}$ ${{z}^{2}}$ $\mathbf{i}z$ $z{{z}^{*}}$

Accepted Answer

(i) $\frac{1}{r}$, $-	heta $ (ii) ${{r}^{2}}$, $2	heta $ (iii) $r$, $\frac{\pi }{2}+	heta $ (iv) ${{r}^{2}}$, $0$

Complex Numbers - Complex Numbers - General

Complex Numbers - Complex Numbers - General