IIT-JEE 2005 Mains | Complex Numbers Question 49 | Mathematics

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

-1

If one of the vertices of the square circumscribing the circle $$|z-1|=\sqrt{2}$$ is $$(2+\sqrt{3 i})$$. Find the other vertices of square.

$$\left( {1 - 2\sqrt 3 } \right) + i,\left( {1 + \sqrt 3 } \right) - i, - \sqrt 3 i$$

$$\left( {1 - \sqrt 3 } \right) + i,\left( {2 + \sqrt 3 } \right) - i, - i$$

$$\left( {1 - \sqrt 3 } \right) + i,\left( {1 + 2\sqrt 3 } \right) - i, - \sqrt 5 i$$

$$\left( {1 - \sqrt 3 } \right) + i,\left( {1 + \sqrt 3 } \right) - i, - \sqrt 3 i$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

If $$\omega $$ $$\left( { \ne 1} \right)$$ be a cube root of unity and $${\left( {1 + {\omega ^2}} \right)^n} = {\left( {1 + {\omega ^4}} \right)^n},$$ then the least positive value of n is

IIT-JEE 2003 Screening

MCQ (Single Correct Answer)

-0.5

If $$\,\left| z \right| = 1$$ and $$\omega = {{z - 1} \over {z + 1}}$$ (where $$z \ne - 1$$), then $${\mathop{\rm Re}\nolimits} \left( \omega \right)$$ is

$$ - {1 \over {{{\left| {z + 1} \right|}^2}}}$$

$$\left| {{z \over {z + 1}}} \right|.{1 \over {{{\left| {z + 1} \right|}^2}}}$$

$$\,{{\sqrt 2 } \over {{{\left| {z + 1} \right|}^2}}}$$

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)

-0.5

For all complex numbers $${z_1},\,{z_2}$$ satisfying $$\left| {{z_1}} \right| = 12$$ and $$\left| {{z_2} - 3 - 4i} \right| = 5,$$
the minimum value of $$\left| {{z_1} - {z_2}} \right|$$ is

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