Identify the locus of `z` if ` bar z = bar a +(r^2)/(z-a).`

Identify the locus of z if z = a +(r^2)/(z-a),> 0.

Identify locus z if R e(z+1)=|z-1|

Let z=x+i ydot Then find the locus of P(z) such that (1+ bar z )/z in Rdot

If Real ((2z-1)/(z+1)) =1, then locus of z is , where z=x+iy and i=sqrt(-1)

If Real ((2z-1)/(z+1)) =1, then locus of z is , where z=x+iy and i=sqrt(-1)

Prove that the circles z bar z +z( bar a _1)+bar z( a_1 )+b_1=0 ,b_1 in R and z bar z +z( bar a _2)+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1 bar a _2)=b_1+b_2dot

If Z is a complex number the radius of z bar z - ( 2+3i)z - (2-3i)barz + 9 =0 is equal to

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.

Given that the complex numbers which satisfy the equation | z bar z ^3|+| bar z z^3|=350 form a rectangle in the Argand plane with the length of its diagonal having an integral number of units, then area of rectangle is 48 sq. units if z_1, z_2, z_3, z_4 are vertices of rectangle, then z_1+z_2+z_3+z_4=0 rectangle is symmetrical about the real axis a r g(z_1-z_3)=pi/4or(3pi)/4

If z=x+i y , then show that z bar z +2(z+ bar z )+a=0 , where a in R , represents a circle.