(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The angles [itex]\theta[/itex] and [itex]\phi[/itex] lie on the interval (-pi/2,pi,2) and

[itex]z=(cos\theta +cos\phi)+i(sin\theta +sin\phi)[/itex]

Show that |z|=2cos([itex]\frac{\theta - \phi}{2}[/itex]) and find arg(z)

2. Relevant equations

If z=x+iy

[tex]|z|=\sqrt{x^2 +y^2}[/tex]

3. The attempt at a solution

[tex]|z|= \sqrt{(cos\theta +cos\phi)^2+(sin\theta +sin\phi)^2}[/tex]

[tex]=2+2cos(\theta - \phi)[/tex]

I don't know how to get rid of the additional two and how to make the angle halved.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: More complex numbers, more trigs

**Physics Forums | Science Articles, Homework Help, Discussion**