\left ({{\sqrt {3} + 1} \over {2}} + i{{\sqrt {3}} - 1 \over {2}} \right ) ^ {20} = \left ( \left ({{\sqrt {3} + 1} \over {2}} + i{{\sqrt {3}} - 1 \over {2}} \right ) ^ {2} \right ) ^ {10} = \dots = \left ({\sqrt {3} + i} \right ) ^ {10}