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1

IIT-JEE 1996

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

Answer

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

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.
3

IIT-JEE 1995

Subjective
If $$i{z^3} + {z^2} - z + i = 0$$ , then show that $$\left| z \right| = 1$$.

Answer

Solve it.
4

IIT-JEE 1990

Subjective
Let $${z_1}$$ = 10 + 6i and $${z_2}$$ = 4 + 6i. If Z is any complex number such that the argument of $${{(z - {z_1})} \over {(z - {z_2})}}\,is{\pi \over 4}$$ , then prove that $$\left| {z - 7 - 9i} \right| = 3\sqrt 2 $$.

Answer

Solve it.

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12