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Let z be a complex number with |z| = 2 and define w = (z + 1)/(z - 1). If M and n are respectively the greatest and least possible values of |w|, compute 2010*n + M.

1. 2013
2. 2010
3. 2011
4. 4023

Correct answer: 2013

Solution

With |z| = 2, the ratio |z+1|/|z-1| is extreme at real z: max = 3, min = 1/3, giving 2010*(1/3) + 3 = 673.

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