Complex Algebra/Examples/(z-1)^6 + (z+1)^6 = 0

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Example of Complex Algebra

The roots of the equation:

$\paren {z - 1}^6 + \paren {z + 1}^6 = 0$

are:

$\pm i \cot \dfrac \pi {12}, \pm i \cot \dfrac {5 \pi} {12}, \pm i$


Proof


Sources