complex number

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If z is a complex number satisfying z+(1/z)=1, calculate z^2+ (1/z^2).

Guest Feb 18, 2021

textot · Answer 1 · 2021-02-19T12:36:38

Square both sides of the first equation:

$(z+\frac{1}{z})^2=1^2\\ z^2+2\cdot z \cdot \frac{1}{z} + \frac{1}{z^2} = 1\\z^2+\frac{1}{z^2}+2=1\\ \boxed{z^2+\frac{1}{z^2}=-1}$