Question

Please help with this

Answer 1

`(\stackrel{a}{-3√(3)}~~,~~\stackrel{b}{-9}) \\\\[-0.35em] ~\dotfill\\\\ r=√(a^2 + b^2)\implies r=\sqrt{(-3√(3))^2 + (-9)^2}\implies r=√(108)\implies r=6√(3) \\\\[-0.35em] ~\dotfill`

`\theta =\tan^(-1)\left( \cfrac{b}{a} \right)\implies \theta = \tan^(-1)\left( \cfrac{-9}{-3√(3)} \right) \\\\\\ \theta = \tan^(-1)(√(3))\implies \theta = \begin{cases} (\pi )/(3)\\[1em] (4\pi )/(3) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill~\left( 6√(3)~~,~~(\pi )/(3) \right)\hspace{5em}\left( 6√(3)~~,~~(4\pi )/(3) \right)~\hfill~`