simple math help

[DT4K]

I know this is easy, but the last math class I took was Calculus III about 10 years ago and I totally forget how to do this stuff.

1/z = 1/a + 1/b

a = 5 + 2i
b = 3 - 4i

How do I solve for z ?

And no, it's not my homework. I'm not even in school.

 

[labrat25]

z = (a*b)/(a+b)

 

[dullard]

It is usually taught to avoid irrational numbers in the denominator (although you don't need to do this, it makes solving things by hand much easier). Thus the first step most people do is to get rid of those. Thus:

1/z = 1/ (5+2i) * (5-2i)/(5-2i) + 1/ (3-4i) * (3+4i)/(3+4i)

Note how I multiplied those by their complex conjugate (replace the + or - sign with the opposite). For example:

1/ (5+2i) = 1/ (5+2i) * (5-2i)/(5-2i) = (5-2i) / [ (5+2i) * (5-2i)] = (5-2i) / [25 +4] = 5/29 + 2i/29

The rest should be a piece of cake if you just keep up that process (you'll need it 3 times).

 

[DT4K]

Thanks.
This is for calculating the impedance of a parallel circuit in case you are wondering.