Given that $\left| z \right|=3$, $\arg z=\frac{\pi }{6}$ and $\left| w \right|=2$, \(\arg

Question

Given that $\left| z \right|=3$, $\arg z=\frac{\pi }{6}$ and $\left| w \right|=2$, $\arg w=-\frac{5\pi }{6}$. Find the modulus and argument of ${{w}^{5}}{{z}^{2}}$ $\frac{{{w}^{2}}}{{{z}^{5}}}$ ${{z}^{-2}}{{w}^{3}}$ $\frac{{{(iw)}^{7}}}{2{{({{z}^{*}})}^{3}}}$ $\frac{{{z}^{*}}{{(1+i)}^{2}}}{w}$

Accepted Answer

(i) modulus $288$, argument $\frac{\pi}{6}$ (ii) modulus $\frac{4}{243}$, argument $-\frac{\pi}{2}$ (iii) modulus $\frac{8}{9}$, argument $-\frac{5\pi}{6}$ (iv) modulus $\frac{64}{27}$, argument $\frac{\pi}{6}$ (v) modulus $3$, argument $-\frac{5\pi}{6}$

Complex Numbers - Modulus, Argument, and Operations on Complex Numbers

Complex Numbers - Modulus, Argument, and Operations on Complex Numbers

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