1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Complex Numbers (Exponential/Rectangular Form)

  1. Aug 30, 2016 #1
    1. The problem statement, all variables and given/known data
    Screen Shot 2016-08-30 at 6.36.48 PM.png

    2. Relevant equations
    Theta = arctan (y/x)

    3. The attempt at a solution
    Hopefully this is the right section to post in, but I am a bit confused with complex numbers. I am working on the problems above and I just wanted to make sure I am doing each part correctly. I think A and B are correct, but I'm not 100% sure about my theta. That usually trips me up. Are my theta's correct? Did I add pi correctly where it needs it? For C and D do I need to include the angle? In my answers? it does not say what form to do C and D in so I was a bit confused about those. Is there a standard form to use when it's not given in the problem? Also, is there some way to simplify D? OR do I just leave it how I have it?

    New Doc 16.jpg
    New Doc 16_2.jpg
  2. jcsd
  3. Aug 30, 2016 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    It looks like you have done parts (a) & (b) correctly.

    Part (c) asks for magnitude, so you're not finished with it.

    Part (d):
    AB is correct.

    I think it's easier to do both AB and A/B using exponential form (also called polar form).

    Change answers to rectangular form at the end.​
  4. Aug 30, 2016 #3
    I thought magnitude only meant the value, without a direction. Is that what I am missing? The direction? If so, how would I find that? Would I have to somehow add the angles I found in part A and B? Angle A + Angle B?

    Oh ok. So since AB is correct I will just leave it. For A/B I can just use the answers from part A and part B right? So when dividing the numbers will just divide like normal but then I can combine the e's to e^(7pi/4 - 5pi/4)j right? Then after that convert to rectangular form? Is that the form you should always go to if the question does not specify?
  5. Aug 30, 2016 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Concerning part (d): The instructions do specify rectangular form.

    When you did parts (a) and (b), you found magnitudes by using right triangles. Do the same for part (c).
  6. Aug 30, 2016 #5


    User Avatar
    2017 Award

    Staff: Mentor

    No. The magnitude is the length. You are asked for ##\vert A+B \vert## and ##\vert A-B \vert##.

    Not always. It's just easier here. Calculate ##A/B## in polar coordinates and you will see what it is in rectangular form.

    SammyS beat me ... but I've done all the calculations, so I couldn't resist ...
  7. Sep 5, 2016 #6
    The magnitude is your ##r## value; other names include the modulus and length. The argument is the ##\theta## value; another name for this is the phase.

    For problems involving ##A/B## in rectangular form, you do not need to convert to exponential form to solve the problem. All you have to do is "rationalize" the denominator. With a complex number as the denominator, you multiply by 1 in the form of the complex conjugate of the denominator. The rest is just simplifying the algebra. Example:

    ##\frac{1}{3+3j} = \frac{1}{3+3j} \times 1 = \frac{1}{3+3j} \times \frac{3-3j}{3-3j} = \frac{3-3j}{(3+3j)(3-3j)} = \frac{3-3j}{18} = \frac{1}{6} - \frac{1}{6}j##
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted