If |z| = 1, express z as a simplified fraction in terms of z.

Since |z| = z z, we have z z = 1. Thus z = 1z.

jmc

algebra intermediate

Problem

∣ z ∣ = 1

, express

\overline{z}

as a simplified fraction in terms of

z

Solution

Since

∣ z ∣ = z \overline{z}

, we have

z \overline{z} = 1

. Thus

\overline{z} = \frac{1}{z}

Final answer

\frac{1}{z}