# Polar form of complex numbers

1. Sep 13, 2010

### madah12

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. Sep 13, 2010

### zhermes

3. Sep 13, 2010

### madah12

uhm so since I like things by examples tell me if I got it right
5+2i
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))?

4. Sep 13, 2010

### zhermes

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.

5. Sep 13, 2010

### madah12

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?

6. Sep 13, 2010

### zhermes

"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)
[tex]
z = f(x+iy)
[\tex]
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.

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