2022 TMJC P2 Q2 [Modified]
It is given that $z=-\sqrt{6}-\text{i}\sqrt{2}$ and $w=3\left( \cos \frac{5\pi }{7}-\text{i}\sin \frac{5\pi }{7} \right)$. Without the use of a calculator, find the modulus and argument of $\frac{\text{i}z{{w}^{2}}}{{{w}^{*}}}$ in exact form.
[6]
Hence, find the three smallest positive values of $n$ for which ${{\left( \frac{\text{i}z{{w}^{2}}}{{{w}^{*}}} \right)}^{n}}$ is purely imaginary.
[2]
Suggested Video Solutions
Share with your friends!
WhatsApp
Telegram
Facebook