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Math Help - Power and root of complex numbers?

  1. #1
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    Power and root of complex numbers?

    Solve each equation. Then graph the root in the complex plane

    x^5+1=0 This is what I did
    x^5=-1
    So that means -1+0i r= square root 1+0 so r=1 theta would be 0/1 or o

    So would the polar form be 1(cos o+ i sin 0)? Did I set this problem up right?

    This is the formula from my textbook I am encouraged to apply
    (a+bi)^(1/p)= r^1/p cos theta+2(n)pi/p+ i sin theta+ 2(n)pi/p
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    Quote Originally Posted by homeylova223 View Post
    Solve each equation. Then graph the root in the complex plane
    x^5+1=0 This is what I did
    x^5=-1
    So that means -1+0i r= square root 1+0 so r=1 theta would be 0/1 or o

    So would the polar form be 1(cos o+ i sin 0)? Did I set this problem up right?
    This is the formula from my textbook I am encouraged to apply
    (a+bi)^(1/p)= r^1/p cos theta+2(n)pi/p+ i sin theta+ 2(n)pi/p
    Yes that is correct to this point.
    However, \theta=\pi NOT ZERO.
    The argument of \mathbf{-1} is \mathbf{\pi}
    Now add to the arguments \dfrac{2\pi k}{5},~k=0,1,2,3,4
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    I am having some difficulties I did this

    =1^(1/5) (cos pi+2pi(0)/5 + i sin pi+2pi(0)/5) This is what I used for k=0 and I got
    -.2+0i
    I am not sure the error that could have been made. I typed in my calculator 1^(1/5)=1
    cos(180)=-1/5=-.2
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  4. #4
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    Quote Originally Posted by homeylova223 View Post
    I am having some difficulties I did this

    =1^(1/5) (cos pi+2pi(0)/5 + i sin pi+2pi(0)/5) This is what I used for k=0 and I got
    -.2+0i
    I am not sure the error that could have been made. I typed in my calculator 1^(1/5)=1
    cos(180)=-1/5=-.2
    You have made two errors:

    1. Using a calculator for such a simple calculation.

    2. Not being able to correctly enter the expression into your calculator.

    As for answering the question, I suggest you give all 5 answers in polar form.
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    I have a new question I need to clarity now that I have solved the question I asked earlier.

    It involved solving this equation 3x^4+48=0 This is what I did
    3x^4+48=0
    3x^4=-48
    x^4=-12

    So in that case -12+0i I got r=12 and theta equals=pi

    Then I plugged in 12^(1/4) (cos pi+2pi(0)/4) + i sin (pi+2pi(0)/4)
    I end up getting 1.861 (.707+.707)
    1.315+1.315i But I think my answer is wrong.

    See I know cos (180/4)=.707
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    Quote Originally Posted by homeylova223 View Post
    I have a new question I need to clarity now that I have solved the question I asked earlier.
    It involved solving this equation 3x^4+48=0
    But I think my answer is wrong.
    You are completely correct: that answer is wrong.
    I do not see how we can help you.
    Did you read Mr. F's reply #4. It is spot on!
    You will never do these problems if you insist on using a calculator.
    Calculator are useless for these problems.

    Here are the answers:
    \sqrt[4]{{16}}\left[ {\cos \left( {\frac{\pi }{4} + \frac{{k\pi }}{2}} \right) + i\sin \left( {\frac{\pi }{4} + \frac{{k\pi }}{2}} \right)} \right],\,k = 0,1,2,3
    Last edited by Plato; April 30th 2011 at 03:17 PM.
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  7. #7
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    Quote Originally Posted by homeylova223 View Post
    I have a new question I need to clarity now that I have solved the question I asked earlier.

    It involved solving this equation 3x^4+48=0 This is what I did
    3x^4+48=0
    3x^4=-48
    x^4=-12

    So in that case -12+0i I got r=12 and theta equals=pi

    Then I plugged in 12^(1/4) (cos pi+2pi(0)/4) + i sin (pi+2pi(0)/4)
    I end up getting 1.861 (.707+.707)
    1.315+1.315i But I think my answer is wrong.

    See I know cos (180/4)=.707
    Look, you have to go back and review basic algebra, arithmetic etc. You have serious problems in these basic areas that are severely impacting on your ability to do questions that require these skills. The fact that you are insisting on using a calculator - incorrectly - is not helping things either. You are probably doing so in order to try and wallpaper over the problems I have mentioned - this is the worst possible reason for using a calculator.

    For starters, -48 divided by 3 is NOT -12. Also, you will be expected to use exact values of the correct value of x. Furthermore, you are expected to use the exact surd value of cos(180/4 degrees) = cos(45 degrees) and sin(45 degrees) and get exact surd values for the cartesian form of the solutions (if cartesian form is required).

    Sorry, but what I have said is a harsh reality - life is not going to get easier by ignoring the problem.
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    Actually thank to Mr. Fantastic pointing my 48/3 mistake I have figured it out the answer is square root 2 plus square root 2 i for n=0

    48/3=16 I guess I typed it incorrectly into my calculator.
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  9. #9
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    Quote Originally Posted by homeylova223 View Post
    Actually thank to Mr. Fantastic pointing my 48/3 mistake I have figured it out the answer is square root 2 plus square root 2 i for n=0

    48/3=16 I guess I typed it incorrectly into my calculator.
    Yet, another good reason for not using a calculator for a problem like that!
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