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# Complex Numbers and Loci Watch

1. So I'm struggling with questions of the form:

Find the locus of the point P, where P represents a complex number z such that

For instance:

As far as I can tell from answers to questions of this form, z describes the arc of a circle that starts at and goes clockwise round to . Let's call these points A and B. The centre of the circle can be determined by noting that the angle AOB = .

In the case of the example I gave (as far as I'm aware), the locus of the point P would look like this.

My problem is that I don't have a clue why this is, or if this is even actually the case. If anybody could help me it would be very much appreciated.

Thanks.
2. Use arg(z/w)=argz-argw and then letting z=x+iy and considering the arg as arctan might help to see where the locus comes from.
3. i find it very difficult to see these loci without a diagram. hope this one helps

baer

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Updated: June 14, 2011
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