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Kool Kid on the block
Kool Kid on the block asked in Science & MathematicsMathematics · 3 years ago

HELP WITH MY TRIG HW: De Moivre’s Theorem *Best Answer Awarded*?

PLEASE Help! Best answer awarded.

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1 Answer

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  • cmcsafe
    Lv 7
    3 years ago

    Express the given number (a+ib) in polar form

    ρ=√(a²+b²)=√(3+1²)=2

    cosθ=a/ρ=-√3/2

    sinθ=b/ρ==1/2

    hence θ=5π/6

    (-√3+i)=ρ(cosθ+isinθ)=

    =2(cos(5π/6)+isin(5π/6))=

    =2cis(5π/6)

    from De Moivre

    (-√3+i)³=2³cis(5π/2)=8*cis(π/2)=8i

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