- #1
miniradman
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Homework Statement
Describe the locus and determine the Cartesian Equation of:
[itex]\left|z-3-5i\right|= 2[/itex]
Homework Equations
[itex]\left|z-C\right|= r[/itex] -----> formula for a circle on complex plane
Where
C = the centre
z = the moving point (locus)
[itex](x-h)^{2}+(y-k)^{2}=r^{2}[/itex] -----> Formula for a circle on the cartesian plane
The Attempt at a Solution
Ok I think I've got the first section, describe the locus
Well if -C = -3-5i
that means C = 3+5i
So the centre of the circle will be at 3+5i on the complex plane.
But I get stuck when converting it into the cartesian form.
[itex]z = x + yi[/itex]
[itex]\left|(x + yi)-3-5i\right|= 2[/itex]
[itex]\sqrt{(x-3)^{2}-i(y + 5)^{2}}[/itex]
[itex]\uparrow[/itex]
But I don't know how to proceede from there because I can't figure out how to get rid of the [itex]i[/itex]
Anyone know how to?