Complex Number (Modulus/Phase)

[Air]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

To find the modulus, I separated 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.

 

[HallsofIvy]

Homework Statement

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.

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

Homework Equations

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

The Attempt at a Solution

To find the modulus, I separated 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.