Determine the locus of `z, z ne 21i` such that Re `((z-4)/(z-2i))=0`

The locus of P(z) satisfying z=x+iy where Re((z-2)/(z-1))=0 is

if |z-1|=|z-i| then locus of z is

The locus of point z satisfying Re (z^(2))=0 , is

What is the locus of z, if amplitude of (z-2-3i) is (pi)/(4)?

Let z be a complex number on the locus (z-i)/(z+i)=e^(i theta)(theta in R) , such that |z-3-2i|+|z+1-3i| is minimum. Then,which of the following statement(s) is (are) correct?

Trace the locus of z if arg(z+i)=(-pi)/(4)

Let I Arg((z-8i)/(z+6))=pmpi/2 II: Re ((z-8i)/(z+6))=0 Show that locus of z in I or II lies on x^2+y^2+6^x – 8^y=0 Hence show that locus of z can also be represented by (z-8i)/(z+6)+(bar(z)-8i)/(barz+6)=0 Further if locus of z is expressed as |z + 3 – 4i| = R, then find R.

If a point P denoting the complex number z moves on the complex plane such tha "Re"(z^(2))="Re"(z+bar(z)) , then the locus of P (z) is