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Consider an ellipse having its foci at A...

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` and 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|))`

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