Simplifying 1/(s+ia) to separate real and imaginary parts

[FrogPad]

Note:
It looks like the LaTeX interpreter is not working right now. So I'll try and use plaintext and make things look pretty.

To my problem:
My algebra skills are kind of weak, but I am trying to show the Laplace transform of cos(at) and I keep getting stuck at this one spot.

it is where
L{e^(i*a*t)} = 1/(s+i*a)

How do I get the complex part out of the bottom? My TI-89 will do it for me automatically... but I can't just turn the solution in like that :)
So the TI-89 says that:

 1           s           a
----   = --------- + --------- i
s+ia      s^2+a^2    s^2+a^2

(or if LaTeX starts working again)
$$\frac{1}{s+ia}=\frac{s}{s^2+a^2}+\frac{a}{s^2+a^2}*i$$

So how the hell is my calc doing that?... partial fractions maybe? I dunno... and it is friggn' bugging me. Thanks in advance.

Sorry about the ascii art :)

 

[siddharth]

Multiply numerator and denominator by (s-ia).
So you will get
s/(s^2+a^2) -ia/(s^2+a^2)

 

[FrogPad]

that was easy

thank you !