Answer
d. $20(\cos25^{\circ}+i\sin25^{\circ})$
Work Step by Step
Recall:
$[r_{1}(\cos\theta_{1}+i\sin\theta_{1})][r_{2}(\cos\theta_{2}+i\sin\theta_{2})]$$=r_{1}r_{2}[\cos(\theta_{1}+\theta_{2})+i\sin(\theta_{1}+\theta_{2})]$
Using the above formula, we have
$5(\cos 10^{\circ}+i\sin10^{\circ})\cdot4(\cos15^{\circ}+i\sin15^{\circ})$$=5\cdot4[\cos(10^{\circ}+15^{\circ})+i\sin(10^{\circ}+15^{\circ})]$
$=20(\cos25^{\circ}+i\sin25^{\circ})$
The correct option is d.
