# Interpret the angle of the complex number

1. Jan 15, 2012

### Baba-k

Hi,

1. The problem statement, all variables and given/known data
Interpret the angle of the complex number $(z_{1} - z_{2}) / (z_{1} - z_{3})$
in the triangle formed by the points $z_{1}, z_{2}, z_{3}$.

2. Relevant equations

3. The attempt at a solution
I'm not entirely sure what to do in this question, I've done a couple of examples with some complex numbers but haven't noticed anything special about the resulting angle. I'm also a bit confused by what 'Interpret' means. Any help with this will be greatly appreciated.

thanks!
babak

2. Jan 15, 2012

### SammyS

Staff Emeritus
In the examples you tried, how does the angle formed at the z1 compare with the argument of $\displaystyle\frac{z_{1} - z_{2}}{z_{1} - z_{3}}\,?$

3. Jan 16, 2012

### genericusrnme

I've seen this question before
if you think about z1-z2, that's just like a vector from z1 to z2, yes

so try and relate the division of the angles to the dot products of normal vectors

4. Jan 22, 2012

### Baba-k

Hi guys,

Thanks for the responses, I think I see now. So the angle formed at $z_{1}$ is the same as the argument of $\frac{z_{1} - z_{2}}{z_{1} - z_{3}}$ ?

thanks
babak