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

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

Find the locus of point z if z , i ,and iz , are collinear.

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

In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2z^2-5z+3)/(3z^2-z-2))}=(2pi)/3dot

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

The locus of z=x+iy satisfying |(z-i)/(z+i)|=2

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

The locus of z=x+iy satisfying |(z-i)/(z+i)|=1

Let vertices of an acute-angled triangle are A(z_1),B(z_2),a n dC(z_3)dot If the origin O is the orthocentre of the triangle, then prove that z_1 bar z _2+ bar z _1z_2=z_2 bar z _3+ bar z _2z_3=z_3 bar z _1+ bar z _3z_1

The locus of any point P(z) on argand plane is arg((z-5i)/(z+5i))=(pi)/(4) . Then the length of the arc described by the locus of P(z) is