Solve the Problem Find $\frac { z } { w }$

question 55

Multiple Choice

Solve the problem. Leave your answer in polar form.
- $$\begin{array} { l } z = 6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right) \\w = 12 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \end{array}$$
Find $\frac { z } { w }$ .

• A) \(\frac { 1 } { 6 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)\)
• B) \(\frac { 1 } { 6 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)\)
• C) \(\frac { 1 } { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)\)
• D) \(\frac { 1 } { 2 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)\)

---

Definitions:

Madness

A term historically used to describe severe mental illness or disorder, often characterized by delusion or hallucination.

-mania

A suffix used to denote an obsession with or excessive enthusiasm for a particular thing or topic.

-plasm

A suffix used in biology to denote a formative or molded substance, such as cytoplasm.

Formed

The past participle of form, indicating something that has been brought into existence or given a specific shape.