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July 17th, 2015, 01:56 AM   #1
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Locus

Hi guys, any help with this one would be great.

Z is a complex number. Sketch the locus of z that satisfied by:

arg(z-2/z-i)=pi/4.

I break this down to:
arg(z-2)-arg(z-i)=pi/4

My thought is to select three points and place them on the imaginary axis, then deduce the coordinate of z, three times, (ie start with z on the im axis, and we can show that coordinate of z is (0,2),then place z-2 on the im axis etc)

Has anyone got an easier way to do this?

I know the answer is a circle, but how can you tell? also, My the answer shows its just a major arc of a circle, but with no explanation as to why only part of the circle exists.

if anyone can help deduce the equation and help with the above I would be appreciate it.

Thanks in advance
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July 17th, 2015, 01:41 PM   #2
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$\displaystyle \frac{z-2}{z-i}=r\frac{\sqrt{2}}{{2}}(1+i)$, where r > 0. Solve for r as a function of z and plot.
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