MathDB
2016 Guts #19

Source:

August 14, 2022
2016Guts Round

Problem Statement

Let z≠0z\neq0 be a complex number satisfying z2=z+i∣z∣z^2=z+i|z|. (∣z∣|z| denotes the length between the origin and zz in the complex plane.) Find z⋅z‾z\cdot\overline{z}, where z‾=a−bi\overline{z}=a-bi is the complex conjugate of z=a+biz=a+bi.
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