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Distance Between Complex Numbers

Source: 2012 AIME II Problem 6

March 29, 2012
inequalitiesgeometrygeometric transformationreflectiontriangle inequalityAMC

Problem Statement

Let z=a+biz = a + bi be the complex number with ∣z∣=5|z| = 5 and b>0b > 0 such that the distance between (1+2i)z3(1 + 2i)z^3 and z5z^5 is maximized, and let z4=c+diz^4 = c + di. Find c+dc+d.
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