need help! (1 Viewer)

[Mathematician]

If two complex numbers intersect at a moving point P with the angle made by the intersection always being the same , how does that make the locus of P( which represents z) a circle ?
(or part of a circle , major /minor arc).


It seems obvious, but i just want some logic. Im wondering why it cant be an ellipse ....

 

[ND]

Have you done circle geometry? This comes from the property that the endpoints of an arc (or chord) subtend the same angle on the circumference (ie. angles in teh same segment are equal).

edit: this does not hold true for an ellipse.

 

[Mathematician]

...

oh yeah.

Since when P moves , the angle subtended from the chord is equal to the angle , the chord subtended in P's other position.

This makes it a circle due to the converse theorem of " angles subtended by the same chord or arc are equal in a circle".

Right ?

 

[ND]

Re: ...

Originally posted by Mathematician

Right ?

Yep.