maths/ physics

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Determine the two square roots of 3+j4 in both a)Cartesian form
b) Polar form

Any help with this question would appreciated

  • maths/ physics -

    let the angle be Ø
    then r = √(3^2+4^2) = 5
    tanØ = 4/3, Ø = .9273

    3 + 4j = 5(cos .9273 + jsin .9273)
    by De Moivre's theorem

    (3 + 4j)^(1/2) = √5(cos ((1/2).9273) + jsin ((1/2).9273))

    = √5( cos .4636 + jsin .4636)

    or 2 + j if expanded.

    check:
    if 2+j is the square root of 3+4j, then
    (2+j)^2 should equal 3+4j

    Left side = (2+j)^2
    = 4 + 4j + j^2
    = 4 + 4j - 1
    = 3 + 4j

    so √(3+4j) = 2+j or √5(cos .4636 + jsin .4636)

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