Question

Write the complex number z = 12+12i in polar format. Select the correct choice below and fill in the answer box(es)

Type an exact answer. Using radicals as needed

Answer 1

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

Check the picture below.