Multiply the Complex Numbers $9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right) 4 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right)$

question 289

Multiple Choice

Multiply the complex numbers.Write the answer in trigonometric form. $9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right) 4 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right)$

• A) \(36 \left( \cos \frac { 67 \pi } { 42 } + i \sin \frac { 67 \pi } { 42 } \right)\)
• B) \(36 \left( \cos \frac { 10 \pi } { 13 } + i \sin \frac { 10 \pi } { 13 } \right)\)
• C) \(36 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)\)
• D) \(13 \left( \cos \frac { 67 \pi } { 42 } + i \sin \frac { 67 \pi } { 42 } \right)\)
• E) \(13 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)\)

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Definitions:

Levator Scapulae

A muscle located in the neck and back that elevates the scapula (shoulder blade).

Serratus Anterior

A muscle on the side of the chest that helps rotate the arm and move it away from the body.

Pectoralis Minor

A thin, triangular muscle located beneath the Pectoralis Major in the chest, involved in functions like scapula downward rotation, depression, and anterior tilt.

Rhomboideus Major

A muscle in the back that is involved in moving the shoulder blades and supporting the arm.