SOLUTION: If z-2i/2z-1 is purely imaginary prove that the locus of z in the Argands diagram is a circle .find centre and radius

Question 1099803: If z-2i/2z-1 is purely imaginary prove that the locus of z in the Argands diagram is a circle .find centre and radius
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

This is a curious type of problem that I have not seen before....

Definitely try to get a second opinion....

Let

Then

Rationalize the denominator by multiplying by its conjugate:

The condition for that number to be purely imaginary is the the real part must be 0:

With the a^2 and b^2 terms with the same coefficient, that is indeed the equation of a circle.

To find the center and radius of the circle, complete the squares in a and b:

The center of the circle is at ((1/4),1); the radius is sqrt(17)/4.

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