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This mock test of Test:- Complex Number - 1 for Mathematics helps you for every Mathematics entrance exam.
This contains 20 Multiple Choice Questions for Mathematics Test:- Complex Number - 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

is equal to

Solution:

QUESTION: 2

is equal to

Solution:

QUESTION: 3

x (-4) is equal to

Solution:

QUESTION: 4

If z = 3 - 2i ; then equals

Solution:

QUESTION: 5

If x + iy = , then (x, y) =

Solution:

QUESTION: 6

The smallest positive integer n for which is real

Solution:

so, smallest positive integer is 2 for which i^{n} will be an integer as i = -1

QUESTION: 7

is equal to

Solution:

**ANSWER :- d**

**Solution :- z = x + iy = (-16 + 30i) ^{1/2}**

**Squaring it we get **

**x ^{2} - y^{2} + 2xyi = -16 + 30 i**

**x ^{2} - y^{2} = -16……………………………….(1)**

**2xy = 30 =>y = 15/x**

**Put the value of y in eq(1)**

**x ^{2}- 225/x^{2} = -16**

**x ^{4} + 16x^{2} -225 = 0**

**x ^{4} + 25x^{2} - 9x^{2} - 225 = 0**

**(x ^{2} + 25) (x^{2} - 9) = 0**

**x = +-3 and y = +-5**

**x + iy = +-(3 + 5i)**

QUESTION: 8

Let z be a purely imaginary number such that Im(z) > 0. Then arg(z) is equal to

Solution:

Let z be the purely imaginary number other than 0 so for z = x + iy, y ≠ 0 but x = 0 so, arg will be tan^{-1} y/ 0 = tan^{-1} ∞ = π/2

QUESTION: 9

Let z be a purely imaginary- number such that Im(z) < 0. Then arg(z) is equal to

Solution:

Let z be the purely imaginary number with (lm)z < 0, so arg(z) is, θ = - π/2

QUESTION: 10

If z be purely real number such that Re(z) < 0, then arg (z) is equal to

Solution:

Let z be the purely real number and Re(z) < 0 then arg(z) = π

QUESTION: 11

Let z be any non - zero complex number. Then arg(z) - is equal to

Solution:

arg(x) + = 0

QUESTION: 12

The complex number (1 + 2i)/(1 - 2i) lies in the

Solution:

= i.e. in the 2nd quadrant

QUESTION: 13

i^{2} + i^{4} + i^{6} + .............. up to (2n + 1) terms

Solution:

i^{2} + i^{4} + i^{6} + ... up to (2n + 1) terms = -1

Note: For i^{2} + i^{4} + i^{6} + ...up to n terms

If n is even then sum = 0

If n is odd then sum = -1

hence i^{2} + i^{4} + i^{6} + ... (2n + 1) term is = -1

QUESTION: 14

Real part of (1 - cosθ + 2i cosθ)^{-1} is

Solution:

Real part of (1 - cosθ + 2: cos θ)^{-1}

So, real part is

QUESTION: 15

The complex number sin x + i cos 2x and cos x - i sin 2x are conjugate to each other for

Solution:

sin x + i cos 2x and cos x - i sin 2x, and their conjugates

sin x - i cos 2x and cos x + i sin 2x will be equal if

cos x: = sin x: ...(i)

=>tan.x:=1

cos 2x sin 2x: ...(ii)

=> tan 2.x = 1

tan x = tan 45

which cannot be satisfied simultaneously

=> no value of x exist.

QUESTION: 16

If xand ty are non - zero real numbers such that x^{2} + y^{2} = 2 then inverse of (x + iy) is equal to -

Solution:

x^{2} + y^{2} = 2

_{
}

QUESTION: 17

For a complex number z,, if and only if -

Solution:

Complex number z, if and only if

QUESTION: 18

is equal to

Solution:

= (w)^{58} + (w^{2})^{58} = w + w^{2} = 1

QUESTION: 19

The equation | z + 3 | = 6 in the complex plane represent

Solution:

| z - 3 | = 6 in the argand plane is

| z - (-3)| = 6 which is the circle where r = 6. and centre (-3,0)

QUESTION: 20

If a ≠ b, then the equation | z - a | + z + b | = 6 in the complex plane represents

Solution:

,

extended portion of line segment.

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