Consider \( \triangle A B C \) in an Argand Plane. Let \( A(0), B(1) \) and \( C(1+i) \) be its ....

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Consider \( \triangle A B C \) in an Argand Plane. Let \( A(0), B(1) \)
\( \mathrm{P} \)
and \( C(1+i) \) be its vertices and \( M \) be the midpoint of \( C A \). Let \( z \) be a variable complex number on the line
W
\( B M \). Let \( u \) be another variable complex number defined as \( u=z^{2}+1 \).

Locus of \( u \) is
(1) Parabola
(2) ellipse
(3) hyperbola
(4) none of these


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