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

If given two complex numbers z_{1}and z_{2}that have arguments [itex]\theta[/itex] and [itex]\phi[/itex], and moduli r and R respectively, then find an expression for the mod-arg form of z_{1}+z_{2}

2. Relevant equations

[tex]z=x+iy=re^{i\theta}=rcis\theta[/tex]

3. The attempt at a solution

I can't seem to find a way to relate z_{1}+z_{2}since I would need to somehow combine the trigonometry terms of:

[tex]z_1+z_2=rcis\theta+Rcis\phi=rcos\theta+Rcos\phi+i(rsin\theta+Rsin\phi)[/tex]

In a similar fashion, [tex]z_1z_2=rcis\theta.Rcis\phi=rRcis(\theta+\phi)[/tex] which does have a relationship. Can I do anything to that equation to find the argument of the new complex number z_{1}+z_{2}?

I'm aware that I can convert both complex numbers into x+iy form and then go from there and also if there are some simple values for r and R, such as r=R then the [itex]arg(z_1+z_2)=(\theta+\phi)/2[/itex]

**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: Complex number arguments

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