Equation OF Line and Circle in Complex Plane.

Straight line and Circle in complex number

What is the equation of the circle in complex plane with radius 2 and centre at 1+i. Does the origin lie within this circle,on the circle or outside it? Does any real number lie on this circle?

Straight line in complex plane

If three complex numbers are in AP.Then,they lie on a circle in the complex plane.

STATEMENT-1 : The differential equation of all circles in a plane can be of order 3. and STATEMENT-2 : General equation of a circle in plane has three independent constant parameters

Equation of line & Complex Slope

On any given are of positive length on the unit circle |z|=1 in the complex plane,

Equation of a straight line on the complex plane passing through a point P denoting the complex number alpha and perpendicular to the vector vec OP where ' O' is the origin can be written as

If (|2z - 3|)/(|z-i|)= k is the equation of circle with complex number 'I' lying inside the circle, find the values of K.

Illustration on Rotation Theorem|| Complex Equation OF Circle and Straight line