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_2k=0,b+2 in R` will intersect orthogonally if `2R e(a_1( bar a )_2)=b_1+b_2dot`

Prove that the circle zbar(z)+zbar(a)_(1)+bar(z)a_(1)+b_(1)=0;b_(1)varepsilon R and zbar(z)+zbar(a)_(2)+bar(z)a_(2)+b_(2)=0;b_(2)varepsilon R will intersect orthogonally if 2Re(a_(1)bar(a)_(2))=b_(1)+b_(2)

If arg (bar (z) _ (1)) = arg (z_ (2)) then

Radius of the circle z bar(z) + (2 + 5.5 i) z + (2-5.5 i) bar(z) + 4 = 0 is ___________

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

If z = x + iy , then show that 2 bar(z) + 2 (a + barz) + b = 0 , where b in R , represents a circles.

The equation zbar(z)+abar(z)+bar(a)z+b=0,b in R represents circle,if