If z = x +iy and ` arg((z-2)/(z+2)) = pi/6` , then find the locus of z.

Statement-1 : The locus of z , if arg((z-1)/(z+1)) = pi/2 is a circle. and Statement -2 : |(z-2)/(z+2)| = pi/2 , then the locus of z is a circle.

If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1 , find the locus of z in the complex plane

Statement-1: If z_(1),z_(2) are affixes of two fixed points A and B in the Argand plane and P(z) is a variable point such that "arg" (z-z_(1))/(z-z_(2))=pi/2 , then the locus of z is a circle having z_(1) and z_(2) as the end-points of a diameter. Statement-2 : arg (z_(2)-z_(1))/(z_(1)-z) = angleAPB

If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then find zdot

If the amplitude of z-2-3i " is " (pi)/(4) , then find the locus of z= x+ yi

If arg z = pi/4 ,then

If arg ((z-6-3i)/(z-3-6i))=pi/4 , then maximum value of |z| :

If arg(z_(1))=(2pi)/3 and arg(z_(2))=pi/2 , then find the principal value of arg(z_(1)z_(2)) and also find the quardrant of z_(1)z_(2) .

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

If z=x+iy and real part ((z-1)/(2z+i))=1 then locus of z is