# Complex Number (Modulus/Phase)

1. Nov 2, 2008

### Air

1. The problem statement, all variables and given/known data
Equation: $\frac{z\theta_0^2}{-\theta^2+ 2i\theta\theta_0\phi+\theta_0^2}$

Where $z, \ \phi$ are constant and $\theta_0$ is the initial theta. Find the modulus and the phase associated with this equation.

2. Relevant equations
$\frac{z\theta_0^2}{-\theta^2+ 2i\theta\theta_0\phi+\theta_0^2}$

3. The attempt at a solution
To find the modulus, I seperated the equation into real and imaginary and multiplied by the conjugate of the imaginary number to get it in the numerator and I got: $=\frac{z\theta^2\phi - z\theta_0^2\phi}{\theta\phi} - \frac{z\theta_0}{2\theta\phi}i$. When doing the modulus, I get: $\sqrt{\frac{4z^2\phi^2\theta^4-8\phi^2z^2\theta^2\theta_0^2+ 4z^2\theta_0^4\phi^2 +z^2\theta_0^2}{4\theta^2}\phi^2}$ and this doesn't seem to simplify too well. Have I made a mistake or is there an easier method which I have missed? Thanks in advance for the help.

Last edited: Nov 2, 2008
2. Nov 2, 2008

### HallsofIvy

Staff Emeritus
Modulus and phase apply to a single complex number. What do you mean by "modulus and phase associated with this equation"?