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 counterclockwise by the argument of w .
B
Scale z by the modulus of w , then rotate clockwise by the argument of w .
C
Scale z by the reciprocal of the modulus of w , then rotate counterclockwise by the argument of w .
D
Scale z by the reciprocal of the modulus of w , then rotate clockwise by the argument of w .
Explanation
Write the complex numbers in polar form: dividing z by w divides their moduli and subtracts their arguments. So z is scaled by 1/|w|, the reciprocal of w’s modulus, and rotated clockwise by the argument of w. This is choice C.
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