Find the Quotient and Write in Rectangular Form $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

question 224

Multiple Choice

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
- $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

• A) \(- \frac { \sqrt { 2 } } { 2 } i\)
• B) \(\frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 } \mathrm { i }\)
• C) \(- \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } \mathrm { i }\)
• D) \(\frac { \sqrt { 2 } } { 2 }\)

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Definitions:

Central Function

The primary or most important role played by a system, organization, or part of the body in its operation or contribution to overall objectives.

Truth Table

A mathematical table used to determine the validity of a proposition by listing all possible logical outcomes.

Symbolic Form

A representation of propositions or arguments using symbols and logical operators to express logical relations clearly and concisely.

Component Statements

The individual assertions or propositions that make up a more complex argument or logical structure.