1. The problem statement, all variables and given/known data The problem states that you need to solve the following equation (without a calculator) : z^5 = z̅ 2. Relevant equations z=a+bi and z̅=a-bi 3. The attempt at a solution So far I've tried multiplying both sides by z̅: z̅ * z^5 = |z̅|^2 (is z̅ * z^5 = z^6 ??) |z|^6 = |z̅|^2 I then divided both sides by |z|^2, but this has lead to an incorrect answer. The answer given is z^6=1 , which then leads to a root of unity equation. Thank you in advance.