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QuizMultiple Choice

Multiply and Divide Complex Numbers — Quiz

Question 1 • Math 4

Which statement describes how to geometrically determine the product of z is equal to 25 minus i and w is equal to square root of 3 plus 3 i on the complex plane?

Answer
A
Stretch z by a factor of square root of 3 and rotate 30 degrees counterclockwise.
B
Stretch z by a factor of 2 square root of 3 and rotate 30 degrees counterclockwise.
C
Stretch z by a factor of square root of 3 and rotate 60 degrees counterclockwise.
D
Stretch z by a factor of 2 square root of 3 and rotate 60 degrees counterclockwise.

Explanation

When multiplying complex numbers, multiply their magnitudes and add their angles. For w = √3 + 3i, its magnitude is √(3 + 9) = 2√3, and its angle is 60° because tan(θ) = 3/√3 = √3. So the product is obtained by stretching z by 2√3 and rotating it 60° counterclockwise.

AI-written and checked against the verified answer.

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