IIT-JEE 2008 Paper 2 Offline | Complex Numbers Question 31 | Mathematics

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

-1

A particle P stats from the point $${z_0}$$ = 1 +2i, where $$i = \sqrt { - 1} $$. It moves horizontally away from origin by 5 unit and then vertically away from origin by 3 units to reach a point $${z_1}$$. From $${z_1}$$ the particle moves $$\sqrt 2 $$ units in the direction of the vector $$\hat i + \hat j$$ and then it moves through an angle $${\pi \over 2}$$ in anticlockwise direction on a circle with centre at origin, to reach a point $${z_2}$$. The point $${z_2}$$ is given by

6 + 7i

-7 + 6i

7 + 6i

- 6 + 7i

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 in $$A \cap B \cap C$$

Then, $${\left| {z + 1 - i} \right|^2} + {\left| {z - 5 - i} \right|^2}$$ lies between :

25 and 29

30 and 34

35 and 39

40 and 44

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

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