Perform the Indicated Operation $3\left(\cos 45^{\circ}+i \sin 45^{\circ}\right) \cdot 5\left(\cos 180^{\circ}+i \sin 180^{\circ}\right)$

Essay

Perform the indicated operation. Give the answer in rectangular form.
(a) $3\left(\cos 45^{\circ}+i \sin 45^{\circ}\right) \cdot 5\left(\cos 180^{\circ}+i \sin 180^{\circ}\right)$
(b) $\frac{5 \operatorname{cis} 60^{\circ}}{4 \operatorname{cis} 30^{\circ}}$
(c) $(4-i)^{4}$
(d) Find the fourth roots of $\sqrt{3}-i$ . Leave your answers in trigonometric form.