JEE Advance - Mathematics (1995 - No. 20)
Let $$z$$ and $$\omega $$ be two complex numbers such that
$$\left| z \right| \le 1,$$ $$\left| \omega \right| \le 1$$ and $$\left| {z + i\omega } \right| = \left| {z - i\overline \omega } \right| = 2$$ then $$z$$ equals
$$\left| z \right| \le 1,$$ $$\left| \omega \right| \le 1$$ and $$\left| {z + i\omega } \right| = \left| {z - i\overline \omega } \right| = 2$$ then $$z$$ equals
$$1$$ or $$i$$
$$i$$ or $$-i$$
$$1$$ or $$ - 1$$
$$i$$ or $$ - 1$$
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