Perform the Indicated Operation $4\left(\cos 90^{\circ}+i \sin 90^{\circ}\right) \cdot 3\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)$

Essay

Perform the indicated operation. Give the answer in rectangular form.
(a) $4\left(\cos 90^{\circ}+i \sin 90^{\circ}\right) \cdot 3\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)$
(b) $\frac{2 \operatorname{cis} 45^{\circ}}{\operatorname{cis} 90^{\circ}}$
(c) $(2+2 i)^{3}$
(d) Find the fourth roots of $2+2 i \sqrt{3}$ . Leave your answers in trigonometric form.