NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

WB JEE 2010

MCQ (Single Correct Answer)

If $$ - \pi < \arg (z) < - {\pi \over 2}$$, then $$\arg \overline z - \arg ( - \overline z )$$ is

A
$$\pi$$
B
$$-$$ $$\pi$$
C
$${\pi \over 2}$$
D
$$ - {\pi \over 2}$$

Explanation

$$\arg (\overline z ) - \arg ( - \overline z ) = \arg \left( {{{\overline z } \over { - \overline z }}} \right) = \arg ( - 1) = \pi $$

2

WB JEE 2010

MCQ (Single Correct Answer)

If $$z = {4 \over {1 - i}}$$, then $$\overline z $$ is (where $$\overline z $$ is complex conjugate of z)

A
2(1 + i)
B
(1 + i)
C
$${2 \over {1 - i}}$$
D
$${4 \over {1 + i}}$$

Explanation

$$\because$$ $$z = {4 \over {1 - i}}$$

$$\therefore$$ $$\overline z = {4 \over {1 + i}}$$

3

WB JEE 2009

MCQ (Single Correct Answer)

For any complex number z, the minimum value of $$|z| + |z - 1|$$ is

A
0
B
1
C
2
D
$$-$$1

Explanation

$$\because$$ $$||{z_1}| - |{z_2}|| \le |{z_1} - {z_2}|$$

$$ \Rightarrow ||z| - 1| \le |z - 1|$$

$$ \Rightarrow - |z - 1| \le |z| - 1| \le |z - 1|$$

$$ \Rightarrow - |z - 1| \le |z| - 1 \Rightarrow 1 \le |z| + |z - 1|$$

So minimum value of $$|z| + |z - 1|$$ is 1

4

WB JEE 2009

MCQ (Single Correct Answer)

The modulus of $${{1 - i} \over {3 + i}} + {{4i} \over 5}$$ is

A
$$\sqrt 5 $$ unit
B
$${{\sqrt {11} } \over 5}$$ unit
C
$${{\sqrt 5 } \over 5}$$ unit
D
$${{\sqrt {12} } \over 5}$$ unit

Explanation

$$z = {{1 - i} \over {3 + i}} + {{4i} \over 5} = {1 \over 5} + {2 \over 5}i$$

$$|z| = \sqrt {{1 \over {25}} + {4 \over {25}}} = {1 \over {\sqrt 5 }} = {{\sqrt 5 } \over 5}$$ units.

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12