Complex Locus (1 Viewer)

[The Nomad]

The quickest method I know:

Assume the locus is defined by Arg(z - a) - Arg(z - b) = x.

If x is positive, the locus of z is the circular arc from a to b in an anti-clockwise direction.
If x is negative, the locus of z is the circular arc from a to b in a clockwise direction.

No need for all them assumptions and calculations.

 

[jet]

Are you going to simply state that in the HSC, draw it and only get a mark? You need to be able to work it out.

 

[The Nomad]

Are you going to simply state that in the HSC, draw it and only get a mark? You need to be able to work it out.

Locus questions tell you to sketch. They don't ask for anything else as far as I know.

And working out suggests using the algebraic method...although for this type of question, a geometric approach is much simpler.

 

[jet]

Locus questions tell you to sketch. They don't ask for anything else as far as I know.

And working out suggests using the algebraic method...although for this type of question, a geometric approach is much simpler.

yes, but you can't just state what the locus is. You need a geometrical argument.