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    NationalHardComplex Numbers10–12

    Which of these is the solution of z3=−8z^{3} = -8 with positive imaginary part?

    Qual destes é a solução de z3=−8z^{3} = -8 com parte imaginária positiva?

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    Solution

    Step 1 of 3

    1. 1.Write −8=8 cis π-8 = 8\,\mathrm{cis}\,\pi. The cube roots have modulus 83=2\sqrt[3]{8} = 2 and arguments π+2kπ3\frac{\pi + 2k\pi}{3}.