Filling Question

If ω=-\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}i, then ω^2+ω^4+ω^4=      

Collected in the board: Imaginary number

Steven Zheng Steven Zheng posted 5 days ago

Answer

  1. If ω=-\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}i, then ω^2=\overline{ω}, ω^3=1


    ω^2+ω^4+ω^4

    =\overline{ω}+ω+1

    =-\dfrac{1}{2}-\dfrac{\sqrt{3}}{2}i+-\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}i+1

    =0

Steven Zheng Steven Zheng posted 5 days ago

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