- #1

rock.freak667

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## Homework Statement

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)

## Homework Equations

If z=x+iy

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

## 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.