​Find the Trigonometric Form of the Complex Number Shown Below

question 14

Multiple Choice

​Find the trigonometric form of the complex number shown below. ​
-7 - i

• A)​ \(5 \sqrt { 2 } \left( \cos \left( \arctan \left( \frac { 2 } { 21 } \right) \right) + i \sin \left( \arctan \left( \frac { 2 } { 21 } \right) \right) \right)\)
• B)​ \(5 \sqrt { 2 } \left( \cos \left( \arctan \left( - \frac { 3 } { 7 } \right) \right) + i \sin \left( \arctan \left( - \frac { 3 } { 7 } \right) \right) \right)\)
• C)​ \[5 \sqrt { 2 } \left( \cos \left( \arctan \left( - \frac { 3 } { 35 } \right) \right) + i \sin \left( \arctan \left( - \frac { 3 } { 35 } \right) \right) \right)\]
• D)​ \(5 \sqrt { 2 } \left( \cos \left( \arctan \left( \frac { 1 } { 7 } \right) \right) + i \sin \left( \arctan \left( \frac { 1 } { 7 } \right) \right) \right)\)
• E)​ \(5 \sqrt { 2 } \left( \cos \left( \arctan \left( \frac { 1 } { 14 } \right) \right) + i \sin \left( \arctan \left( \frac { 1 } { 14 } \right) \right) \right)\)

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Definitions:

Color Family

A group of colors that share certain characteristics, such as warmth or coolness, allowing them to blend well together.

Cooler Temperatures

Lower than average ambient temperatures, often perceived as refreshing or cold.

Cool Colors

Colors perceived as calming and soothing, often associated with shades of blue, green, and purple.

Appropriate Level

The suitable or recommended intensity or degree of a condition, activity, or measurement.