Precalculus · Problem 10

Rational Functions — Stitz & Zeager

Mathematics — Precalculus · complex-number-arithmetic

Problem

For

z = -\dfrac{\sqrt{2}}{2} + \dfrac{\sqrt{2}}{2}i

w = -\dfrac{\sqrt{2}}{2} - \dfrac{\sqrt{2}}{2}i

, find and simplify the following. Write your answers in the form

a + bi

z + w, \quad zw, \quad z^2, \quad \frac{1}{z}, \quad \frac{z}{w}, \quad \frac{w}{z}, \quad \bar{z}, \quad z\bar{z}, \quad (\bar{z})^2