IIT-JEE 2008 Paper 1 Offline | Complex Numbers Question 36 | Mathematics

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IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let A, B, C be three sets of complex numbers as defined below :

$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$

$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$

$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$

The number of elements in the set $$A \cap B \cap C$$ is

$$\infty $$

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Let A, B, C be three sets of complex numbers as defined below

$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$

$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$

$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$

Let z be any point $$A \cap B \cap C$$ and let w be any point satisfying $$\left| {w - 2 - i} \right| < 3\,$$. Then, $$\left| z \right| - \left| w \right| + 3$$ lies between :

- 6 and 3

- 3 and 6

- 6 and 6

- 3 and 9

IIT-JEE 2007

MCQ (Single Correct Answer)

-0.75

If $$\left| z \right|\, =1\,and\,z\, \ne \, \pm \,1,$$ then all the values of $${z \over {1 - {z^2}}}$$ lie on

a line not passing through the origin

$$\left| z \right|\, = \,\sqrt 2 $$

the x-axis

the y-axis

IIT-JEE 2007

MCQ (Single Correct Answer)

-0.75

A man walks a distance of 3 units from the origin towards the north-east ($$N\,{45^ \circ E }$$) direction. From there, he walks a distance of 4 units towards the north-west $$\left( {N\,{{45}^ \circ }\,W} \right)$$ direction to reach a point P. Then the position of P in the Argand plane is

$$3{e^{i\pi /4}} + 4i$$

$$\left( {3 - 4i} \right){e^{i\pi /4}}$$

$$\left( {4 + 3i} \right){e^{i\pi /4}}$$

$$\left( {3 + 4i} \right){e^{i\pi /4}}$$

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