Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 32

EASY

NDA & NA EE

IMPORTANT

Earn 100

The locus of the point $z = x + i y$ satisfying $|\frac{z - 2 i}{z + 2 i}| = 1$ is

50% studentsanswered this correctly

Important Questions on Complex Numbers

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 33

The complex number

z

satisfying the equations

|z| - 4 = |z - i| - |z + 5 i| = 0

is

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 34

The common roots of the equations

z^{3} + 2 z^{2} + 2 z + 1 = 0

and

z^{1985} + z^{100} + 1 = 0

are

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NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 35

If

α

is an

n^{th}

root of unity other than unity itself, then the value of

1 + α + α^{2} + \dots + α^{n - 1}

is equal to

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 36

If

\frac{|z - 2|}{|z - 3|} = 2

represents a circle, then its radius is

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 37

If

z = 1 + i . \tan α

, where

π < α < \frac{3 π}{2}

, then what is

|z|

equal to?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 38

The smallest positive integral value of

n

for which

{(\frac{1 - i}{1 + i})}^{n}

is purely imaginary with positive imaginary part is

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 39

The points

z_{1}, z_{2}, z_{3}

and

z_{4}

in the complex plane are the vertices of a parallelogram taken in order if and only if

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 6 - Complex Numbers>PRACTICE EXERCISE>Q 40

If

2 x = 3 + 5 i

, then what is the value of

2 x^{3} + 2 x^{2} - 7 x + 72

?