IIT-JEE 2008 Paper 1 Offline | Complex Numbers Question 42 | Mathematics

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 Paper 2 Offline

MCQ (Single Correct Answer)

-1

If $$|z|=1$$ and $$z \neq \pm 1$$, then all the values of $$\frac{z}{1-z^{2}}$$ lie on

a line not passing through the origin

$$|z|=\sqrt{2}$$

the X-axis

the Y-axis

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-1

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 (N 45$$^\circ$$W) direction to reach a point P. Then the position of P in the Argand plane is

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

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

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

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

IIT-JEE 2006

MCQ (Single Correct Answer)

-1

If $$w=\alpha+\mathrm{i} \beta$$, where $$\beta \neq 0$$ and $$z \neq 1$$, satisfies the condition that $$\left(\frac{w-\bar{w} z}{1-z}\right)$$ is purely real, then the set of values of $$z$$ is:

$$\{z:|z|=1\}$$

$$\{z: z=\vec{z}\}$$

$$\{z: z \neq z\}$$

$$\{z:|z|=1, z \neq 1 \mid\}$$

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