Find all circles which are orthogonal to `|z|=1and|z-1|=4.`

The locus of the center of a circle which touches the circles |z-z_1|=a, |z-z_2=b| externally will be

The locus of the centre of a circle which touches the given circles |z -z_(1)| = |3 + 4i| and |z-z_(2)| =|1+isqrt3| is a hyperbola, then the lenth of its transvers axis is ……

All complex numbers 'z' which satisfy the relation |z-|z+1||=|z+|z-1|| on the complex plane lie on the

IF agt=1 , find all complex numbers z satisfying the equation z+a|z+1|+i=0

If the complex number z is such that |z-1|le1 and |z-2|=1 find the maximum possible value |z|^(2)

z_1a n dz_2 lie on a circle with center at the origin. The point of intersection z_3 of he tangents at z_1a n dz_2 is given by 1/2(z_1+( z )_2) b. (2z_1z_2)/(z_1+z_2) c. 1/2(1/(z_1)+1/(z_2)) d. (z_1+z_2)/(( z )_1( z )_2)

Solve for z , i.e. find all complex numbers z which satisfy |z|^2-2i z+2c(1+i)=0 where c is real.

lf z_1,z_2,z_3 are vertices of an equilateral triangle inscribed in the circle |z| = 2 and if z_1 = 1 + iotasqrt3 , then

The value of lambda for which the inequality |z_(1)/|z_(1)|+z_(2)/|z_(2)|| le lambda is true for all z_(1),z_(2) in C , is

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 , find the minimum value of |z_1-z_2|