Find the locus of point z in the Argand plane if ` (z-1)/(z+1)` is purely imaginary.

If the number (z-1)/(z+1) is purely imaginary, then

if z-bar(z)=0 then z is purely imaginary

If the ratio (1-z)/(1+z) is purely imaginary, then

if |(1-iz)/(z-i)|=1 prove that the locus of the variable point z in the Argand plane is the real axis.

If the imaginary part of (2z+1)/(iz+1) is -2, then show that the locus of the point respresenting z in the argand plane is a straight line.

If |z+3i|+|z-i|=8 , then the locus of z, in the Argand plane, is

A(z_(1)) and B(z_(2)) are two fixed points in the Argand plane and P(z) is variable point satisfying |z-z_(1)|=k|z-z_(2)| , where k gt 0 and k ne 1 . The locus of is