Let $ Z_1 $ and $ Z_2 $ be complex numbers such that $ {4Z_2} $ is purely imaginary. What is $ \left| {Z_1 - Z_2} \right| $ equal to ?

Question

SquadPrep · Accepted Answer

1. If Z_1/Z_2 is purely imaginary, the magnitudes of Z_1/Z_2 + 1 and Z_1/Z_2 - 1 are equal, making the modulus of their ratio 1.

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2

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{2}

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{4}

Let \( Z_1 \) and \( Z_2 \) be complex numbers such that \( \frac{3Z_1}{4Z_2} \) is purely imaginary. What is \( \left| \frac{Z_1 + Z_2}{Z_1 - Z_2} \right| \) equal to ?