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Math Help - complex number help

  1. #1
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    complex number help

    could somone help me do this math problem, i've got all the information i think i need, but i cannot get the right answer. its for a math make-up, would really appriciate your help. thanks.

    Info:
    A=rcosΘ
    B=rsinΘ
    Z=A+Bi = (rcosΘ+isinΘ)
    tanΘ=B/A
    r=sqrt((A^2)+(B^2))

    Problem: Find all the square roots of the complex number Z= -1/2 - (sqrt3)/2. You can use polar coordinates but convert them back to retangular form for the answer.
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  2. #2
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    Hello,zabije cie!

    Are you allowed to use DeMoivre's Theorem?


    Find the square roots of: .Z .= .-½ - (½√3)i

    The polar form is: .Z .= .cos(4π/3) + i·sin(4π/3)

    Then: .Z^½ .= .±[cos(2π/3) + i·sin(2π/3)] .= .±[-½ + (½√3)i]

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  3. #3
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    umm yes we are, could you show work how u did it? btw a square root would have two answers right?
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  4. #4
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    Hello again, zabije cie!

    DeMoivre's Theorem says: .(cosθ + i·sinθ)^n .= .cos(nθ) + i·sin(nθ)

    In baby-talk: the exponent "jumps in and joins the angle".


    We have: θ = 4π/3 and n = ½

    [cos(4π/3) + i·sin(4π/3)]^½ .= .cos(½·4π/3) + i·sin(½·4π/3) .= .cos(2π/3) + i·sin(2π/3)


    And I do have two square roots . . . did you see the ± ?

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  5. #5
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    whyd you do it to the power of 1/2???? i thought youd do power 1 and power 2?
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