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Thread: Find a product - give answer in polar form

  1. #1
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    Question Find a product - give answer in polar form

    given

    Z1= 2-2i Z2= (square root of 3)-i

    i need help finding the answers for

    Z1*Z2 and Z1/Z2

    needs to find polar complex
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  2. #2
    Junior Member lanzailan's Avatar
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    z1=2-2j
    =2.828/_-45 <<----polar form

    z2=(3)^-1/2-j
    =2/_-30 <<----- polar form

    z1*z2=(2.828*2)/_-45+(-30)
    =5.656/_-75

    z1/z2=2.828/2*/_-45-(-30)
    =1.414/_-15
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  3. #3
    MHF Contributor

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    The polar form that lanzailan gives is r and the angle (in degrees). For problems like this it is better to give the angle in radians: These complex numbers can be written as 2\sqrt{2}(cos(\frac{\pi}{4})- sin(\frac{\pi}{4}), 2(cos(\frac{\pi}{6})+ sin(\frac{\pi}{6}), or, equivalently, 2\sqrt{2}e^{i\frac{\pi}{4}} and 2e^{i\frac{\pi}{6}}.

    To find the product of two complex numbers, in complex form, you multiply the moduli (r values) and add the angles. To divide, divide the moduli and subtract the angles.
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