Why Poles move to LOWER Half Plane

[Master J]

Pretty simple question here guys, but I can't get my head around it.

When solving say, the Greens Function for the driven harmonic oscillator, one needs to use the Residue method of integration. So, one adds a complex quantity to your variable w (angular frequency), so we now have w ---> w + iy .

This moves the poles into the LOWER half plane. But why is that. I would have intuitately thought them to move to the UPPER half plane since we are adding and not subtracting a complex quantity.

Can someone shed some light on this?

 

[Master J]

Perhaps I should restate my question...

Say I am integrating a function with cos(x) - E in the denominator, where E is a constant. So I have poles at:

cos(x) - E = 0

or

x = cos^-1(E)

so how do I assign the locations of these poles in the complex plane. I know that they are in the upper left and lower right portions, but I cannot see how this?

 

[Stephen Tashi]

I can't tell if you are asking a completely simple question, but I only have an answer for a simple question, so here goes:

Say you have a graph of the function f(x) of a single real variable and you want to move that graph 1 unit to the right along the x-axis. Which function would you plot, f(x+1) or f(x-1)?

It's rather like daylight savings time adjustments. Spring forward, fall back. If want to move the graph a(x) of your daytime activity to the left in Spring so that you get up earlier then set your clock forward and use a(x+1).