2
practice testMultiple Choice

Practice Test

Question 2 • Math 4

Which phrase describes how to divide a complex number z by r times open paren cosine theta plus i sine theta close paren ?

Answer
A
Scale by a factor of 1 over r and rotate clockwise by theta .
B
Scale by a factor of r and rotate counterclockwise by theta .
C
Scale by a factor of 1 over r and rotate counterclockwise by theta .
D
Scale by a factor of r and rotate clockwise by theta .

Explanation

Dividing by r(cos θ + i sin θ) is the same as multiplying by its reciprocal, which is (1/r)(cos θ − i sin θ). The factor 1/r scales the complex number by 1/r, and the angle −θ rotates it clockwise by θ. Therefore, the correct description is “Scale by a factor of 1 over r and rotate clockwise by theta.”

AI-written and checked against the verified answer.

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