5
QuizMultiple Choice

Multiply and Divide Complex Numbers

Question 5 • *PGHS Precalculus B

Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?

Answer
A
Scale z by the modulus of w, then rotate clockwise by the argument of w.
B
Scale z by the modulus of w, then rotate counterclockwise by the argument of w.
C
Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
D
Scale z by the reciprocal of the modulus of w, then rotate counterclockwise by the argument of w.

Explanation

Write the complex numbers in polar form: z = |z|e^(iθ) and w = |w|e^(iφ). Then z/w = (|z|/|w|)e^(i(θ−φ)), so division scales z by the reciprocal of |w| and subtracts w’s argument, which is a clockwise rotation. Thus, the correct statement is “Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.”

AI-written and checked against the verified answer.

Previous
Next