Factoring algebraic complex expression

1. Jul 23, 2014

Maxo

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
We can factor the variable 'a' which gives:
a(c+di)-bd+bci
The common factor in the remaing terms is b, and if we also factor out b we get
a(c+di)-b(d+ci)

But this is not the way I want it factorized. I want it to be factored completely. How can that be done step by step?

2. Jul 23, 2014

Fightfish

Do you realise the similarity between the factors (c+di) and (d-ci)? How can you make them the same?

Last edited: Jul 23, 2014
3. Jul 23, 2014

Maxo

I made a misstake, it should be a(c+di)-b(d-ci). Anyway so you're saying (c+di) and (d-ci) can be made the same. I actually don't see how that could be done? I mean both the real and the imaginary parts of these expressions are different. How are they the same?

4. Jul 23, 2014

Fightfish

Maybe I wasn't very clear with what I meant by "make the same", but what I was trying to convey is identifying the common factor between these two terms. Notice that they differ by a factor of i

5. Jul 23, 2014

MrAnchovy

For your second step, factor out bi instead of just b. Be more careful with signs and brackets.

6. Jul 23, 2014

Maxo

Now I see it :)

Is there some rule (algorithm) / procedure to follow when factoring like this?