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
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.
Complex Numbers and Loci
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Last edited by porkstein; 13-06-2011 at 20:40.
- 13-06-2011 20:31
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- 13-06-2011 22:13
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.
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- 14-06-2011 11:53
i find it very difficult to see these loci without a diagram. hope this one helps