Transfer function to impulse response

[yoran]

Homework Statement

Given the transfer function of a linear, time-invariant system
H(z)=\frac{z^2+5z}{z^2+5}
compute the impulse response.

Homework Equations

We are supposed to compute the inverse z-transform with partial fraction decomposition but the problem here is the irreducible quadratic function z^2+5.

The Attempt at a Solution

In our table of inverse z-transforms they are only functions of the the type
\frac{z^{m+1}}{(z-a)^{m+1}}
I tried this.
H(z)=\frac{z^2+5z}{z^2+5}=\frac{z^2}{z^2+5}+5\frac{z}{z^2+5}
I can compute the inverse z-transform of \frac{z^2}{z^2+5} just fine, but how do I compute the inverse z-transform of \frac{z}{z^2+5}

Thanks.

 

[jhicks]

It's not irreducible. z^2+5=(z-\sqrt{5}i)(z+\sqrt{5}i). Complex numbers are an important part of z transforms.

 

[yoran]

Ok thank you now I think I can solve it.