Answer
$30.8580+18.5414i$
Work Step by Step
First, we use the product theorem to multiply the absolute values and add the arguments:
$(12$ cis $18.5^{\circ})(3$ cis $12.5^{\circ})$
$=12(3)$ cis $(18.5^{\circ}+12.5^{\circ})$
$=36$ cis $(31.0^{\circ})$
Next, we change the expression into its equivalent form:
$36$ cis $(31.0^{\circ})$
$=36 (\cos 31^{\circ}+i\sin 31^{\circ})$
Then, we use the calculator to solve the functions of $\cos$ and $\sin$ and simplify the expression:
$36 (\cos 31^{\circ}+i\sin 31^{\circ})$
=$36 [0.857167+i(0.515038)]$
=$30.8580+18.5414i$
