Interpret the angle of the complex number

[Baba-k]

Hi,

Homework Statement

Interpret the angle of the complex number [itex](z_{1} - z_{2}) / (z_{1} - z_{3})[/itex]
in the triangle formed by the points [itex]z_{1}, z_{2}, z_{3}[/itex].

Homework Equations

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

 

[SammyS]

Hi,

Homework Statement

Interpret the angle of the complex number [itex](z_{1} - z_{2}) / (z_{1} - z_{3})[/itex]
in the triangle formed by the points [itex]z_{1}, z_{2}, z_{3}[/itex].

Homework Equations

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

In the examples you tried, how does the angle formed at the z₁ compare with the argument of [itex]\displaystyle\frac{z_{1} - z_{2}}{z_{1} - z_{3}}\,?[/itex]

 

[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

 

[Baba-k]

Hi guys,

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

thanks
babak