Consider an ellipse having its foci at `A(z_1)a n dB(z_2)` in the Argand plane. If the eccentricity of the ellipse be `e` an it is known that origin is an interior point of the ellipse, then prove that `e in (0,(|z_1-z_2|)/(|z_1|+|z_2|))`

Consider an ellipse having its foci at A(z_(1)) and B(z_(2)) in the Argand plane.If the eccentricity of the ellipse be e an it is known that origin is an interior point of the ellipse, then prove that e in(0,(|z_(1)-z_(2)|)/(|z_(1)|+|z_(2)|))

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

Eccentricity of the ellipse |z-4| + |z-4i| = 10 sqrt(2) is __________

The condition for the points z_1,z_2,z_3,z_4 taken in order in the Argand plane to be the vertices of a parallelogram is

Let z_1 nez_2 are two points in the Argand plane if a abs(z_1)=b abs(z_2) then point (az_1-bz_2)/(az_1+bz_2) lies

The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior of an ellipse (2) exterior of a circle (3) interior and boundary of an ellipse (4) none of these

The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior of an ellipse (2) exterior of a circle (3) interior and boundary of an ellipse (4) none of these

The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior of an ellipse (2) exterior of a circle (3) interior and boundary of an ellipse (4) none of these