Answer
$\frac{3\sqrt 3}{2}-\frac{3}{2}i$
Work Step by Step
We know that $\cos30^{\circ}=\frac{\sqrt 3}{2}$ and $\sin30^{\circ}=\frac{1}{2}$
Substituting these values in the expression and solving:
$3(\cos30^{\circ}+i\sin30^{\circ})=3(\frac{\sqrt 3}{2}-\frac{1}{2}i)=\frac{3\sqrt 3}{2}-\frac{3}{2}i$
Therefore, the rectangular form is $\frac{3\sqrt 3}{2}-\frac{3}{2}i$.
