Mathegoras

Complex numbers › Complex arithmetic › Dividing complex numbers

Real part of reciprocal on unit circle

University · ●●○○○ 20 pts

Let zz be a complex number with ∣z∣=1|z| = 1 and z≠−1z \neq -1. Show that Re⁡(1z+1)\operatorname{Re}\left(\frac{1}{z+1}\right) is a constant, and find its value.

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complex conjugate