Solve the equation `z^(3) = barz (z ne 0)`

Explanation

To solve the equation \( z^3 = \bar{z} \) where \( z \neq 0 \), we can follow these steps:

### Step 1: Rewrite the equation in terms of modulus
We know that the modulus of a complex number \( z \) is given by \( |z| = \sqrt{a^2 + b^2} \) where \( z = a + bi \). The conjugate \( \bar{z} \) has the same modulus as \( z \), so we can write:
\[ |z^3| = |\bar{z}| \]
Since \( |\bar{z}| = |z| \), we have:
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