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Kosovo Mathematical Olympiad, #1 (Grade 12) [Complex Number]

Source:

March 13, 2011
complex numbersalgebra proposedalgebra

Problem Statement

The complex numbers z1z_1 and z2z_2 are given such that z1=−1+iz_1=-1+i and z2=2+4iz_2=2+4i. Find the complex number z3z_3 such that z1,z2,z3z_1,z_2,z_3 are the points of an equilateral triangle. How many solutions do we have ?
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