[tex]a + bi ~~=~~ r[\cos(\theta )+i\sin(\theta )] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{a}{12}~+~\stackrel{b}{12}i\qquad \begin{cases} tan(\theta )&=\frac{b}{a}\\ \theta &=tan^{-1}\left( \frac{b}{a} \right)\\ &=tan^{-1}\left(\frac{12}{12} \right)\\ &=tan^{-1}(1)\\ &=\frac{\pi }{4}\\[2em] r &=\sqrt{a^2+b^2}\\ &=\sqrt{12^2+12^2}\\ &=\sqrt{288}\\ &=12\sqrt{2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill z = 12\sqrt{2}\left[ \cos\left( \frac{\pi }{4} \right)+i\sin\left( \frac{\pi }{4} \right) \right]~\hfill[/tex]
Check the picture below.
