" 9.यदि "|z+1|=sqrt(2)|z-1|" So prove that the point makes a circle. "

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z lies on the circle whose centre is the point (1)/(2) (1+i) and radius is (1)/(sqrt2)

If z_(2) be the image of a point z_(1) with respect to the line (1-i)z+(1+i)bar(z)=1 and |z_(1)|=1 , then prove that z_(2) lies on a circle. Find the equation of that circle.

If z_(2) be the image of a point z_(1) with respect to the line (1-i)z+(1+i)bar(z)=1 and |z_(1)|=1 , then prove that z_(2) lies on a circle. Find the equation of that circle.

Prove that if the ratio (z - i)/( z - 1) is purely imaginary then the point z lies on the circle whose centre is at the point 1/2(1+i)and " radius is " 1/sqrt(2)

If |z|=1 , then prove that the points represented by sqrt((1+z)/(1-z)) lie on one or other of two fixed perpendicular straight lines.

If |z-3i|

If z_1^2+z_2^2-2z_1.z_2.costheta= 0 prove that the points represented by z_1, z_2 , and the origin form an isosceles triangle.