- #1
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Homework Statement
If given two complex numbers z1 and z2 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 z1+z2
Homework Equations
[tex]z=x+iy=re^{i\theta}=rcis\theta[/tex]
The Attempt at a Solution
I can't seem to find a way to relate z1+z2 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 z1+z2?
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]