Trying to understand the whole picture in my head.

[MrAlbot]

Homework Statement

so.. I'm taking a electrotechnical engeneering at university and now I'm talking a lot about telecomunitactions and i find myself working with Fourier transforms and laplace transforms, and majorly, the e^(jx)... and this last one shakes up my concept of the usual number raised to the power. and i don't understand how it works graphicly.

i've been drawing all sorts of graphs trying to explain and put it into my head how this works graphicly but without any luck.

i've tryed going back to the point where i define in my head, how does the sqrt(a) function works, after i go into negative numbers.

Assuming that a is a real number, I decided to draw 3 axis, one for x, other for y and a ne one for Imaginary parts. ( assuming the real one is contabilizated by the x axxis)... did work once i had only an imaginary part in my resulting number like 4j for x=-4, 30j for x= -30 , 50j for x= -50.

Then i tryed to understand what happens when i have something like y=x^2+2x+2 and the result of y= 0 is 1±i (if I'm not mistaken) and i stared to plot a graphic only in Y axis and getting a result in Re and I am numbers (so, i had 3 axis). so I'm assuming x is unknown and I'm plotting the function over the complex plane, and analysing it.So now you know how badly i wan't to understand it because my head its not functioning until something clicks here and makes some sense to me.Sorry for not using a very understandable way to explain myself. I'm just not into that deep mathematical definitions, still i feel like if i have to know evrything so my head is t peace ill learn it right away!

Hope someone can help me.

Thanks in advance!

edit: sorry for missing all the titles i should have followed, this is my first post here , and I'm not used to ask mathematic doubts to people, so it might be very confusing at glance.

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

so.. I'm taking a electrotechnical engeneering at university and now I'm talking a lot about telecomunitactions and i find myself working with Fourier transforms and laplace transforms, and majorly, the e^(jx)... and this last one shakes up my concept of the usual number raised to the power. and i don't understand how it works graphicly.

i've been drawing all sorts of graphs trying to explain and put it into my head how this works graphicly but without any luck.

i've tryed going back to the point where i define in my head, how does the sqrt(a) function works, after i go into negative numbers.

Assuming that a is a real number, I decided to draw 3 axis, one for x, other for y and a ne one for Imaginary parts. ( assuming the real one is contabilizated by the x axxis)... did work once i had only an imaginary part in my resulting number like 4j for x=-4, 30j for x= -30 , 50j for x= -50.

Then i tryed to understand what happens when i have something like y=x^2+2x+2 and the result of y= 0 is 1±i (if I'm not mistaken) and i stared to plot a graphic only in Y axis and getting a result in Re and I am numbers (so, i had 3 axis). so I'm assuming x is unknown and I'm plotting the function over the complex plane, and analysing it.


So now you know how badly i wan't to understand it because my head its not functioning until something clicks here and makes some sense to me.


Sorry for not using a very understandable way to explain myself. I'm just not into that deep mathematical definitions, still i feel like if i have to know evrything so my head is t peace ill learn it right away!

Hope someone can help me.

Thanks in advance!

edit: sorry for missing all the titles i should have followed, this is my first post here , and I'm not used to ask mathematic doubts to people, so it might be very confusing at glance.

Homework Equations

The Attempt at a Solution

One thing you MUST avoid is the multiple use of the letter 'i': when you are talking about complex numbers and i = √(-1) and the like, NEVER use i to mean 'I' (that is, *myself*). This is one place where being lazy and not pushing the 'shift' key can be dangerous!

Anyway, it is not clear from your submission whether you are having trouble understanding complex numbers, or whether your problems come later. Assuming that complex numbers themselves are giving you a headache, why not look at some on-line sources, such as
http://en.wikipedia.org/wiki/Complex_number or
http://tutorial.math.lamar.edu/Extras/ComplexPrimer/ComplexNumbers.aspx (especially the later section on polar form) or
http://www.clarku.edu/~djoyce/complex/