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## Homework Statement

Find the partial fractions expansion in the following form,

[tex]G(s) = \frac{1}{(s+1)(s^{2}+4)} = \frac{A}{s+1} + \frac{B}{s+j2} + \frac{B^{*}}{s-j2}[/tex]

## Homework Equations

## The Attempt at a Solution

I expanded things out and found the following,

[tex]1 = A(s^{2} + 4) + B(s^{2} + (1-j2)s -j2) + B^{*}(s^{2} + (1+j2)s + j2)[/tex]

From this I get the following equations,

[tex]A + B + B^{*} = 0[/tex]

[tex]B(1-j2) + B^{*}(1+j2) = 0[/tex]

[tex]4A - Bj2 + B^{*}j2 = 1[/tex]

This doesn't seem like a pleasant set of equations to solve.

I did another partial fractions expansion like so,

[tex]G(s) = \frac{1}{(s+1)(s^{2}+4)} = \frac{D}{s+1} + \frac{Es + F}{s^{2}+4}[/tex]

and found,

[tex]D = \frac{1}{5}, E = - \frac{1}{5}, F = \frac{1}{5}[/tex]

but this doesn't give me the form I need.

Any ideas? Any convenient ways to solve this?