Given that $\left| z \right|=5$, $\arg z=\frac{\pi }{3}$ and $\left| w \right|=7$, \(\arg

Question

Given that $\left| z \right|=5$, $\arg z=\frac{\pi }{3}$ and $\left| w \right|=7$, $\arg w=-\frac{\pi }{2}$. Find the modulus and argument of ${{z}^{2}}w$ $\frac{{{z}^{*}}}{{{w}^{4}}}$ ${{w}^{-3}}{{({{z}^{*}})}^{2}}$ $2\text{i}{{z}^{5}}$ $\frac{{{w}^{3}}}{{{\left( z\mathbf{i} \right)}^{4}}}$

Accepted Answer

(i) modulus $175$, argument $\dfrac\pi6$ (ii) modulus $\dfrac5{2401}$, argument $-\dfrac\pi3$ (iii) modulus $\dfrac{25}{343}$, argument $\dfrac{5\pi}{6}$ (iv) modulus $6250$, argument $\dfrac\pi6$ (v) modulus $\dfrac{343}{625}$, argument $-\dfrac{5\pi}{6}$

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

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

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