Solve a Complex Number Question: z = a/b and 1/(a+b) = 1/a + 1/b?

[lockedup]

Homework Statement

If $$z = \frac{a}{b}$$ and $$\frac{1}{a + b} = \frac{1}{a} + \frac{1}{b}$$, find z.

Homework Equations

I'm pretty sure z is a complex number.

The Attempt at a Solution

I have no idea where to start. The teacher did nothing like this in class. I tried something that involved combining the fractions on the right hand side and then cross-multiplying with the fraction on the left hand side. I played around with that for a few minutes but it didn't give me anything.

 

[PhysicsMark]

I am confused about what you are asking. z is defined. Are you trying to get z in different terms than above? Or perhaps in cartesian/standard or polar form?

 

[l'Hôpital]

I tried something that involved combining the fractions on the right hand side and then cross-multiplying with the fraction on the left hand side. I played around with that for a few minutes but it didn't give me anything.

Keep playing. It works out.

 

[Dick]

Multiply both sides of your equation by (a+b) and try to reduce the right side to terms that are constants or a/b, or b/a. a/b=z. Doesn't that make b/a=1/z? Write it all in terms of z. Think 'quadratic equation'.

 

[lockedup]

I think I got it. I substituted zb for a. I combined and cross multiplied again. I ended up with $$z = \frac{-1}{2} \pm \frac{i\sqrt{3}}{2}$$

Now I need to check it...

 

[lockedup]

It checks! w00t \O/