Given that $| z |=3,\arg z=\dfrac{\pi }{6}$ and $| w |=2,\arg w=-\dfrac{5\pi }{6}$. Find the modulus

Question

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

Accepted Answer

(i) $144\sqrt{3}+144i$; (ii) $-\frac{4i}{243}$; (iii) $-\frac{4\sqrt{3}}{9}-\frac{4i}{9}$; (iv) $\frac{32\sqrt{3}}{27}+\frac{32i}{27}$; (v) $-\frac{3\sqrt{3}}{2}-\frac{3i}{2}$

Properties from Exponential or Trigonometric form Q1

Properties from Exponential or Trigonometric form Q1

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