Question about converting polar to rectangular in complex numbers

Discussion in 'Math' started by hunterage2000, May 15, 2010.

  1. hunterage2000

    Thread Starter Active Member

    May 2, 2010
    400
    0
    I have a question I cant work out

    If v=200V(rms) angle-(35) and i = 10A(rms) angle-(-20), calculate the impedance in rectangular form. Is it:

    A 11.47 + j16.38
    B 15.32 - j12.85
    C 18.12 + j8.45
    D 6.84 - j18.79
     
  2. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    The topic of math on complex variables is well covered in the AAC ebook.

    hgmjr
     
  3. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    You should be able to do this nearly in your head (i.e., without a calculator) from knowing the elementary rules of complex numbers in polar form. The impedance magnitude is 20 ohms and the angle is 55 degrees (assuming the angles are measured in degrees). Now 55 degrees is nearly 60 degrees and you should have the sine and cosine of 60 degrees memorized (sine is sqrt(3)/2 and cosine is 1/2). Assuming 60 degrees and converting to rectangular coordinates, we get one coordinate is about 17.3 and the other is about 10. If you know how the trig functions change, then the answer is obvious. There are only two possible answers in the above set of four and it's obvious which one it is (I'll let you work out the details).

    Tiny Tim throws his calculator away! :p
     
  4. Wendy

    Moderator

    Mar 24, 2008
    20,766
    2,536
    Never! You will pry my calculator away from my cold dead hands!
     
  5. kingdano

    Member

    Apr 14, 2010
    377
    19

    this

    i <3 my TI-89
     
  6. ma1991

    New Member

    May 19, 2010
    1
    0
    z=R^2+JXl-JXc
     
  7. S_lannan

    Active Member

    Jun 20, 2007
    247
    2
    When it comes to working with complex numbers even the best calculators including my ti-89 have had a nasty habit of getting it wrong. Always use common sense when dealing with complex numbers. Eg 10 + j5 will always fall in a certain quadrant.
     
  8. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Can you give an example that might go wrong? I have my HP35s feeling rather insulted by this rebuke!
     
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