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

question 72

Multiple Choice

Solve the problem. Leave your answer in polar form.
- $$\begin{array} { l } z = \sqrt { 3 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right) \\w = \sqrt { 6 } \left( \cos \frac { 9 \pi } { 4 } + i \sin \frac { 9 \pi } { 4 } \right) \end{array}$$
Find $\frac { z } { w }$ .

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

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Definitions:

Helium

A chemical element with symbol He, the second lightest element, known for being a colorless, odorless, tasteless, non-toxic, inert gas.

Open System

A system that exchanges both energy and matter with its surroundings, characteristic of most natural and biological systems.

Closed System

A physical system that does not exchange matter with its surroundings, though it may exchange energy.

Penetrating Radiation

Radiation that can penetrate through substances and materials, potentially causing ionization of atoms.