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Let z1 and z2 be complex numbers satisfying |z1| = 12 and |z2 - (sqrt(3) + i)| = 5 respectively. Find the range of values of |z1 - z2|.

1. [6, 18]
2. [5, 19]
3. [5, 13]
4. [6, 19]

Correct answer: [5, 19]

Solution

The point z2 lies on a circle of radius 5 centred at sqrt(3)+i (which has modulus 2). So |z2| ranges from 0 to 7. With |z1|=12, the triangle inequality gives |z1-z2| in [12-7, 12+7] = [5, 19].

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