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Math Help - complex numbers

  1. #1
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    complex numbers

    During my university course my instructor has taught us how to do the following type of question and I understand how to do it..
    Evaluate square root of z z=-5+j12 then using Pythagoras and trig the angle comes out at 13<1.966 rads.
    < = angle.
    Using the following formula z^1/2 = 13^1/2 <(tan^-1 12/5 +k2pie)/2 and letting k = 0 and 1 respectively I eventually come up with 1.999 + j3.001 and -1.999 j3.001 as my roots of the above question..
    I understand this..
    However I now have the question find the roots of complex number z^4= 1-sqrt 3
    In this instance do I do the same as above..
    i.e r = sqrt (1^2+(sqrt3)^2) =2 Theta =2pie tan^-1 sqrt3/1 = 5.236 rads.
    Let k=0 z^4= 2^4<(5.236 + (0 * 2pie)*4 = 20.944
    = 16<20.944 I need to divide this by 2pie to fit into a circle
    = 16 < 3.333
    Using the formula r(cos theta + j sin theta) this = -15.717 j 2.997
    Following rest through using the above method, k=1,2,3 respectively I get
    16<1.050 giving 7.961 +j 13.879
    16<5.05 giving 5.299-j 15.098
    16<0.267 giving 15.346 + j4.53
    Is this the correct method to use to tackle this problem.. Any advice will be greatly appreciated.
    Many thanks in advance
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jawa7539 View Post
    During my university course my instructor has taught us how to do the following type of question and I understand how to do it..
    Evaluate square root of z z=-5+j12 then using Pythagoras and trig the angle comes out at 13<1.966 rads.
    < = angle.
    Using the following formula z^1/2 = 13^1/2 <(tan^-1 12/5 +k2pie)/2 and letting k = 0 and 1 respectively I eventually come up with 1.999 + j3.001 and -1.999 j3.001 as my roots of the above question..
    I understand this..
    However I now have the question find the roots of complex number z^4= 1-sqrt 3
    In this instance do I do the same as above..
    i.e r = sqrt (1^2+(sqrt3)^2) =2 Theta =2pie tan^-1 sqrt3/1 = 5.236 rads.
    Let k=0 z^4= 2^4<(5.236 + (0 * 2pie)*4 = 20.944
    = 16<20.944 I need to divide this by 2pie to fit into a circle
    = 16 < 3.333
    Using the formula r(cos theta + j sin theta) this = -15.717 j 2.997
    Following rest through using the above method, k=1,2,3 respectively I get
    16<1.050 giving 7.961 +j 13.879
    16<5.05 giving 5.299-j 15.098
    16<0.267 giving 15.346 + j4.53
    Is this the correct method to use to tackle this problem.. Any advice will be greatly appreciated.
    Many thanks in advance
    It is hard to read this. Is the question find \sqrt{12i-5}?
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