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Variable complex number z satisfies the ...

Variable complex number z satisfies the equation `|z-1+2i|+|z+3-i|=10`. Prove that locus of complex number z is ellipse. Also, find the centre, foci and eccentricity of the ellipse.

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To solve the problem step by step, we will analyze the given equation and derive the properties of the ellipse. ### Step 1: Rewrite the given equation The given equation is: \[ |z - (1 - 2i)| + |z - (-3 + i)| = 10 \] This can be interpreted as the sum of the distances from the variable complex number \( z \) to the points \( z_1 = 1 - 2i \) and \( z_2 = -3 + i \). ...
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