The locus of z such that `arg[(1-2i)z-2+5i]= (pi)/(4)` is a

The locus of z such that |(1+iz)/(z+i)|=1 is

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)/(2z^2-z-2))}=(2pi)/3dot

Represents the variable complex number z . Find the locus of P if arg((z-1)/(z+3))=(pi)/(2) .

The modulus of the complex number z such that |z+3-i|=1" and "arg z= pi is equal to

If z = x + iy and arg ((z - i)/(z + 2))= (pi)/(4) . Show that x^(2) + y^(2) + 3x - 3y + 2 = 0 .

Find the center of the arc represented by a r g[(z-3i)//(z-2i+4)]=pi//4 .

Obtain the Cartesian form of the locus of z in each of the following cases. (i) |z| = |z - i| " " (ii) |2z - 3 - i| = 3

Let z_1=10+6i and z_2=4+6idot If z is any complex number such that the argument of ((z-z_1))/((z-z_2)) is pi/4, then prove that |z-7-9i|=3sqrt(2) .