1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Question about adding complex numbers

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data

    I was working on a problem dealing with complex numbers. I had to add two phasors together to get the combined phasor. I converted both numbers to rectangular form, added them and converted the result back to polar form. My magnitude was correct, but my phase was not.

    2. Relevant equations

    rectangular form of both complex numbers added together: -1.204 + j0.9476.

    magnitude : 1.532.

    phase: -38.2043 degrees

    book answer: 1.532e^j141.79

    3. The attempt at a solution

    I don't really understand why I didn't get the phase right. I took the arctan of y / x and got the wrong answer. Just for the heck of it, I decided to randomly add 180 to my phase and got 141.79. What effect did this have? Why did I need to add 180? How was I supposed to know I needed to add 180?

    Thanks
     
  2. jcsd
  3. Feb 6, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    tan(141.79) and tan(-38.2043) both give you the same y/x. The tip off is that the polar form of 141.79 will be in the second quadrant (negative x and positive y). The polar form of -38.2043 is in the fourth quadrant (positive x and negative y). arctan can't tell the difference. You can if you look at the original number. You want the second quadrant one.
     
  4. Feb 6, 2010 #3
    rectangular form of both complex numbers added together: -1.204 + j0.9476.

    tell you that it is r=-ve this give the phasor in the second quadrant.

    your -38.2043 is from -ve r-axis to the phasor. The angle from +ve r-axis is 180-38.2043=141.79. Which is the same as the answer.
     
  5. Feb 6, 2010 #4

    Hmm, that makes sense. The weird thing is, i took arctan manually with my calculator and got -38.2043. However, when I put the entered the number into my calculator as rectangular and let the calculator convert it to polar, it knew to print 141.79.
     
  6. Feb 6, 2010 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    When you used the polar converter it knew x was positive and y was negative. If you just put in y/x there is no way to tell the signs of x or y.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook