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1

IIT-JEE 1999

Subjective
For complex numbers z and w, prove that $${\left| z \right|^2}w - {\left| w \right|^2}z = z - w$$ if and only if $$ z = w\,or\,z\overline {\,w} = 1$$.

Answer

solve it.
2

IIT-JEE 1997

Subjective
Let $${z_1}$$ and $${z_2}$$ be roots of the equation $${z^2} + pz + q = 0\,$$ , where the coefficients p and q may be complex numbers. Let A and B represent $${z_1}$$ and $${z_2}$$ in the complex plane. If $$\angle AOB = \alpha \ne 0\,$$ and OA = OB, where O is the origin, prove that $${p^2} = 4q\,{\cos ^2}\left( {{\alpha \over 2}} \right)$$.

Answer

solve it.
3

IIT-JEE 1996

Subjective
Find all non-zero complex numbers Z satisfying $$\overline Z = i{Z^2}$$.

Answer

$$i,{{ \pm \sqrt 3 } \over 2} - {i \over 2}$$
4

IIT-JEE 1995

Subjective
If $$\left| {Z - W} \right| \le 1,\left| W \right| \le 1$$, show that $${\left| {Z - W} \right|^2} \le {(\left| Z \right| - \left| W \right|)^2} + {(ArgZ - Arg\,W)^2}$$

Answer

solved it.

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Class 12