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    NationalHardComplex Numbers10–12

    Trigonometric Form and a Sixth Power

    Forma Trigonométrica e Sexta Potência

    Let z = 1 + i\sqrt{3}. Write z in trigonometric form and compute z^{6}.

    Both the modulus and an argument are needed before any power can be taken, and the argument depends on which quadrant the point sits in. Once the trigonometric form is in place, raising to a power treats the modulus and the argument differently.

    Solution

    Step 1 of 5

    1. 1.|z| = \sqrt{1^{2} + (\sqrt{3})^{2}} = \sqrt{4} = 2