Find all the complex square roots of w= 36(cos60°+ isin60°). Write the roots in polar form with θ in degrees.

Question

Find all the complex square roots of w= 36(cos60°+ isin60°). Write the roots in polar form with θ in degrees.

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Skylar 2 weeks 2021-09-10T08:14:27+00:00 1 Answer 0

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    2021-09-10T08:15:29+00:00

    Answer:

    3√3+i3

    Step-by-step explanation:

    w= 36(cos60°+ isin60°)

    √w = w^{1/2}=√36(cos60°+ isin60°)

    =6√(cos60°+ isin60°)

    now using DeMoivre’s theorem

    =(cos60°+ isin60°)^{1/2}

    =(cos60°/2+ isin60°/2)=(cos30°+ isin30°)

    w^{1/2}=6(cos30°+ isin30°)

    =6(sqrt3/2+i1/2)\sqrt{frac{3}{2} }

    =3√3+i3

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