Answer
$-30i$
Work Step by Step
Step 1: $[5(\cos90^{\circ}+i\sin90^{\circ})][6(\cos180^{\circ}+i\sin180^{\circ}]$
Step 2: Using the product theorem, the expression becomes
$5(6)[\cos(90^{\circ}+180^{\circ})+i\sin(90^{\circ}+180^{\circ})]$
Step 3: Simplifying, $30(\cos270^{\circ}+i\sin270^{\circ})$
Step 4: We know that $\cos270^{\circ}=0$ and $\sin270^{\circ}=-1$
Step 5: Substituting these values in the expression, $30(0+i(-1))$
Step 6: Therefore, the final answer is $-30i$.
