Let Z₁ and Z₂ be complex numbers such that 3Z₁/(4Z₂) is purely imaginary. What is |(Z₁ + Z₂)/(Z₁ − Z₂)| equal to?
A.2
B.3/2
C.5/4
D.1✓ Correct
Explanation
If 3Z₁/(4Z₂) is purely imaginary, then Z₁/Z₂ is purely imaginary, say Z₁/Z₂ = ik for some real k. Then (Z₁ + Z₂)/(Z₁ − Z₂) = (ik + 1)/(ik − 1). Its modulus is √(k² + 1)/√(k² + 1) = 1.
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