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Modulus and argument

  1. May 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the modulus and argument of
    1) cos(i)
    2) -3i

    2. Relevant equations

    3. The attempt at a solution
    1) So for question 1 i tried
    cos(i) = ½(ei2 + e-i2) = ½(e-1 + e) . However this doesn't (as far as I can see!) lead me to the right answer. I was aiming to get it in the form reix where r is the modulus and x the argument.

    for 2) I basically just drew an argand diagram and found the radius to be 3 and the argument 3/4pi.

    if you could point me in the right direction with 1 especially that would be greatly appreciated!
  2. jcsd
  3. May 13, 2016 #2


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    Concerning 1: what you have done is the right direction.
    cos(i) = ½(e-1 + e) is correct.
    Now the question is: why do you think this is not in the form reix?
  4. May 13, 2016 #3


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    Why 3π/4? How many radians does it take to go around a circle one time?
  5. May 13, 2016 #4
    I was thinking it contains no term with i. But would ½(e-1 + e) be equal to the modulus and have an argument of o?
  6. May 13, 2016 #5


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  7. May 13, 2016 #6
    Oops 3π/2?
  8. May 13, 2016 #7
    Thank you!
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