# Complex Number Division and Addition

1. Sep 14, 2015

### Sirsh

1. The problem statement, all variables and given/known data
This is not for a mathematics unit but is part of an electrical question I'm trying to solve but I cannot solve this equation. The complex numbers Zp and Zr are both real and imaginary, whereas Xm is purely imaginary.

2. Relevant equations
Zp = (Xm*Zr)/(Xm+Zr)

Zp = 29.76+j15.72
Xm = j95

3. The attempt at a solution

Zp = (Xm*Zr)/(Xm+Zr)
Zp(Xm+Zr) = (Xm*Zr)
Zp*Xm + Zp*Zr = Xm*Zr
(Zp*Xm)/Xm + (Zp*Zr)/Xm = Zr
Zp + (Zp*Zr)/Xm = Zr

I just do not know how to get Zr on it's own then I can approach solving it, either way i see it will have Zr on either sides of the equation. So even before substituting i feel it is the wrong approach.

2. Sep 14, 2015

### andrewkirk

When you get to here, you have one term involving Zr on each side of the equation.

Do you know how to move the one on the left side across to the right side?

If you can do that then the distributive law is your friend, and will help you home.

By the way, the fact that the numbers are complex has no effect on the method.

3. Sep 15, 2015

### Sirsh

I have never heard of the distributive law before, but have applied it naturally when doing maths I think.

I can re-arrange the equation and get this I think:

Zp*Xm + Zp*Zr = Xm*Zr

Zp*Xm = Xm*Zr - Zp*Zr
Zp*Xm = Zr(Xm-Zp)
(Zp*Xm)/(Xm-Zp)=Zr

Is this correct? I can then substitute my values into this and solve for Zr?

4. Sep 15, 2015

Yep!