[Astrokel]

Hey guys,

I'm having problems with complex number and a few friends and my teachers say it is an easy chapter, i find it not so. Perhaps i'm not grasping the concepts or practicing enough. I'm aware of math forums on other forum but i'd prefer here as i hardly visit other forums.

I don't understand the geometrical effects of conjugating a complex number and of adding, subtracting, multplying and dividing two complex numbers on argand diagrams. Can you point me to a good website or help me with it? I guess it is not easy to teach math here?

Thanks in advance! 

[azmanam]

I don't really have much to offer except to link to a few pages that talk about manipulating complex numbers.

http://en.wikipedia.org/wiki/Complex_number
http://www.sosmath.com/complex/number/basic/soscv.html
http://www.college-cram.com/study/algebra/presentations/268

I don't know if those are what you're looking for or not.

But the real reason I responded is to post this video about new math.  Now, it is probably not safe for work, but is still pretty funny.  He talks about i and Santa in the middle, so make sure you listen for that

Take this as your official CONTENT WARNING.

http://boortz.com/more/video/new_math.html

[Astrokel]

hey azmanam,

though it is not what i'm asking for, still i thank you for the reply and the video!;D It's funny!! and for those interested in the lyrics its here http://vids.myspace.com/index.cfm?fuseaction=vids.individual&videoid=35524789 

[enahs]

The geometric interpretation of the complex conjugate is is reflection of Z (the complex number) in the real axis.

You will have to be a little more specific with your questions.

It is best to just start small. Say you live in a one dimensional world, and so you have the X-Axis. Think of the Imaginary-Axis as a person living in a two dimensional world would of a Y-Axis.

[nj_bartel]

I think enahs meant a Z axis.

[Yggdrasil]

Geometric interpretation of addition:
Represent the complex number as a point on the plane in cartesian coordinates (the normal (x,y) coordinate system).  For example, z = a + bi can be represented by (a,b).  Now consider two complex numbers z₁ = a + bi = (a,b) and z₂ = c + di = (c,d).  As you would expect, z₁ + z₂ = (a+c) + (b+d)i = (a+c,b+d).  In other words, complex numbers add just like two vectors would.

Geometric interpretation of multiplication:
In addition to representing complex numbers in cartesian coordinates, we can represent them in polar coordinates, (r,θ), where r is the distance of the point from the origin and θ is the angle made by the vector and the positive x-axis.  One can convert to polar coordinates from cartesian coordinates by the formula r = (x²+y²)^(1/2) and tanθ = y/x.  The opposite conversion is given by x = r cosθ, y = r sinθ.

When multiplying two complex numbers z₁ = (r₁, θ₁) and z₂ = (r₂, θ₂), you multiply the radial components and add the angular components: z₁z₂ = (r₁r₂,θ₁+θ₂). 

This fact comes from the fact that complex numbers can be written as z = re^iθ.


Also, as enahs said, conjugation is just reflection of the point across the real axis (i.e. the x-axis).

[Astrokel]

thanks Yggdrasil, Enahs and nj_bartel! 

If division of 2 complex number will result in (r1/r2,θ1-θ2), am i right? How do i draw multiplication and division of two complex number on an argand diagram? I find the angle which is from the real axis and find x and y? I think i'm able to grasp some of the concepts, i will try out some problems now!

thanks again!!