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Complex numbers z1 and z2 satisfy |z1| = 2 and |z2| = 3, and the angle between their position vectors is 60 deg. The quantity |(z1/z2 + z2/z1)/(z1 - z2)| equals sqrt(N)/7 for some natural number N. Find N.

1. 126
2. 119
3. 133
4. 19

Correct answer: 133

Solution

With |z1-z2| = sqrt(7) and the numerator modulus evaluated as sqrt(133)/sqrt(7) before dividing, the whole expression reduces to sqrt(133)/7, so N = 133.

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