Square of Complex Conjugate is Complex Conjugate of Square
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Theorem
Let $z \in \C$ be a complex number.
Let $\overline z$ denote the complex conjugate of $z$.
Then:
- $\overline {z^2} = \left({\overline z}\right)^2$
Proof
A direct consequence of Product of Complex Conjugates:
- $\overline {z_1 z_2} = \overline {z_1} \cdot \overline {z_2}$
for two complex numbers $z_1, z_2 \in \C$.
$\blacksquare$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.2$. The Algebraic Theory