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Complex numbers simplification

  1. Jan 24, 2016 #1
    • Member warned about posting unclear question with missing information
    1. The problem statement, all variables and given/known data
    Z=((2z1)+(4z2))/(z1)(z2) where Z1=4e^2pi/3
    Z2=2/60 degre, z3=1+i
    The answer must be in polar form r/theta



    2. Relevant equations
    Well in the upper section

    3. The attempt at a solution
    After do some operations i get to this and unable to convert to polar form... - i((squarert3+1)/2) i need some help, the polar form go to infinite when i apply arctan(y/x)
     
    Last edited by a moderator: Jan 24, 2016
  2. jcsd
  3. Jan 24, 2016 #2
    I don't see a question.
     
  4. Jan 24, 2016 #3
    The thread implies, the "question" or in this case an issue whit the problem stated at the start, so i need to convert my answer to polar form but i cant because one C/0 so i need to know if i have a good answer and its not possible to convert to polar or if i did some mistake in operating the complex numbers
     
  5. Jan 24, 2016 #4

    SammyS

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    We should not have to guess what your question is. A complete statement of the problem should be given in the body of the post which initiates the thread, no matter what is the thread's title.

    I addition to that, It looks as if you have some typographical errors in the statement of your problem.

    What do you mean by " Z2=2/60 degre, " ?

    What is z3 to be used for?

     
  6. Jan 24, 2016 #5
    Oh sorry you are right z3 its for (2z1+4z3)/z1z2, and z2 its in the polar form
    Where 2=r and 60=theta
     
  7. Jan 24, 2016 #6

    SammyS

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    z1 looks like it was written in a form close to being in polar form except that there is an i (imaginary unit) missing from the exponent.

    Is it intended that ##\displaystyle \ z_1=4e^{2\pi i/3} \ ## ?
     
  8. Jan 24, 2016 #7
    yes sorry again i assume the imaginary unit will be implicit in the exponential form of complex numbers, well doing my research, appears to be correct and the polar form will be: in the form Rθ being theta= -90 so tell me if i am correct, or incorrect please, just to finish properly my homework :)
     
  9. Jan 24, 2016 #8

    Mark44

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    No, that's not true. ##e^{2\pi/3}## is a real number, and ##e^{2i\pi/3}## is a complex number.
     
  10. Jan 24, 2016 #9
    Sorry for that
     
  11. Jan 24, 2016 #10

    SammyS

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    Is that ##\displaystyle \ -i\frac{\sqrt{3}+1}{2}\ ##, or something else? (You have been a bit careless with parentheses.)

    For what values of θ, is tan(θ) undefined (sort of like being infinite)?
     
  12. Jan 24, 2016 #11
    Yes that its my finale answer, and for the indetermination of theta i use the form thetha=arctan(y/x) so if my answer its pure complex number, so y/0 its infinite right? For r the value exist for thetha doesn't exist
     
  13. Jan 24, 2016 #12
    Being x the real part and y the complex in the form x+yi
     
  14. Jan 24, 2016 #13

    SammyS

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    How do you convert polar form, let's say 2/60°, to the form, x + yi ?
     
  15. Jan 24, 2016 #14
    Whit the form x=rcosthetha y=rsinthetha
    To the form x+yi
     
  16. Jan 24, 2016 #15

    SammyS

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    Fine.

    So what does θ need to be to get x = 0 and get y to be negative (actually -r) ?
     
  17. Jan 24, 2016 #16
    It must be in 90 degres to get rcos90=0, but i dont get the think of - r
     
  18. Jan 24, 2016 #17

    SammyS

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    Well sin(90°) = 1 , so 90° won't do what's needed.

    What does θ need to be for sin(θ) = -1 ? What is cosine for this θ ?
     
  19. Jan 24, 2016 #18
    I guess - 90 degrees to get the both answers
     
  20. Jan 24, 2016 #19

    SammyS

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    Correct.

    Does that work out for the problem you're working on in this thread?
     
  21. Jan 24, 2016 #20
    Yes then i must say the polar form of my complex number its given by R=√((√3+1)/2)^2 and thetha=-90 degres by definition
     
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