Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Polar form of complex numbers

  1. Sep 13, 2010 #1
    I know that a complex number can be written in form of a+bi and r(cos(theta) + isin(theta))
    but I don't understand the the representation of it as r*e^(i * theta) also
  2. jcsd
  3. Sep 13, 2010 #2
  4. Sep 13, 2010 #3
    uhm so since I like things by examples tell me if I got it right
    in polar form its
    5.4 (isin(tan^-1(2/5)+.cos(tan^-1(2/5)
    and it could be written as 5.4e^(i*tan^-1(2/5))?
  5. Sep 13, 2010 #4
    Yeah! thats exactly right.

    If you imagine that complex numbers are a position in the x-y plane, where the x-axis is real numbers and the y-axis is imaginary numbers; then a+ib is just a standard rectilinear (Cartesian) way of describing a point [e.g. 5+2i = 5x + 2y = (5,2) ]; when you use r*e^{i\theta}, its like writing it in polar coordinates, r is the magnitude, and theta the angle with the x-axis.
  6. Sep 13, 2010 #5
    is it possible with the rectangular coordinate to graph a complex function? I searched the net but couldn't figure out the right key words I mean like f(x)=2x+2ix and you input (2-i) and get 6+2i or does no such thing exist in mathematics?
  7. Sep 13, 2010 #6
    "Complex functions" are the general term for functions which operate on (or yield) complex numbers. But note, you have to input two scalars (the equivalent of a complex number)
    z = f(x+iy)
    You, therefore, can't graph such functions in 2 dimensions, because you have 2 input dimensions (e.g. x and y) and then output dimensions (1 if your result is a real number, and 2 if your result is a complex number).

    If you have a function which takes a complex number and gives a real number, you could plot it as a surface in 3 dimensions.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook