For the complex numbers z = 30 (cosine (StartFraction 2 pi Over 3 EndFraction) + I sine (StartFraction 2 pi Over 3 EndFraction) ) and w = 6 (cosine (StartFraction pi Over 8 EndFraction) + I sine (StartFraction pi Over 8 EndFraction) ) , which geometric transformation of z on the complex plane describes the quotient StartFraction z Over w EndFraction ?

Scale z by a factor of One-sixth, then rotate clockwise by StartFraction pi Over 8 EndFraction radians.
Scale z by a factor of 6, then rotate clockwise by StartFraction pi Over 8 EndFraction radians.
Scale z by a factor of One-sixth, then rotate counterclockwise by StartFraction pi Over 8 EndFraction radians.
Scale z by a factor of 6, then rotate counterclockwise by StartFraction pi Over 8 EndFraction radians.

The geometric transformation of z that describes the quotient z/w is A. Scale z by a factor of 1/6, then rotate clockwise by pi/8 radians.

Geometric transformation

It should be noted that transformation means change. Therefore, a geometric transformation means changes in a geometric shape.

From the complete information, the complex numbers z = 30 (cos(2pi/3) + sin(2pi/3)) and w = 6 (cos(pi/8) + sin(pi/8).

The geometric transformation of z on the complex plane that describes the quotient z/w will be to scale z by a factor of 1/6, then rotate clockwise by pi/8 radians.

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