Practice question on complex number for IIT-JEE , NDA and Airforce

COMPLEX NUMBER

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Question no. 1

The amplitude of 0

looks_one 0

looks_two π/2

looks_3 π

looks_4 none of these

Option looks_one 0

The amplitude of 0
Given : Z= 0, it means no imginary part
if we assume 'zero' a small positive number
it will be on +ve axis and make 0 degree angle

Question no. 2

The amplitude of (1+√3i)/(√3+i) is

looks_one π/3

looks_two -π/3

looks_3 π/6

looks_4 -π/6

Option looks_3 π/6

Question no. 3

The complex number (1+2i)/(1-i) lies in which quadrant of the complex plane

looks_one First

looks_two Second

looks_3 Third

looks_4 Fourth

Option looks_two Second

Question no. 4

If x= cosB + i sinB , then =

looks_one cotB

looks_two cot(B/2)

looks_3 icot(B/2)

looks_4 itan(B/2)

Option looks_3 icot(B/2)

Formula : 2cos²x = 1 + cos2x
sin2x = 2sinxcosx
2 sin²x = 1 - cos2x
Solution :

Question no. 5

If = x+iy , then

looks_one x=2, y=-1

looks_two x=0 ,y=1

looks_3 x=1 , y=0

looks_4 x=-1 , y=2

Option looks_3 x=1 , y=0

Question no. 6

The conjugate of 1+i is

looks_one i-1

looks_two 1-i

looks_3 -1-i

looks_4 None of these

Option looks_two 1-i

Conjugate of 1+i is 1-i ( for conjugate , change the sign of imaginary part )

Question no. 7

If z= then arg(z)=

looks_one 60^o

looks_two 120^o

looks_3 240^o

looks_4 300^o

Option looks_one 60^o

Question no. 8

The amplitude of the complex number z= sinB + i(1-cosB) is

looks_one B

looks_two B/2

looks_3 2sin(B/2)

looks_4 None of these

Option looks_two B/2

Question no. 9

If ā be the conjugate of the complex number a then which of the following relations is false

looks_one |a|=|ā|

looks_two a.ā=|ā|²

looks_3 arg(a)=arg(ā)

looks_4 none of these

Option looks_3 arg(a) = arg(ā)

|a|=|ā| is correct
a.ā=|ā|² is correct
but arg(a) ≠ arg(ā)

Question no. 10

If is purely imaginary , then

looks_one 3/2

looks_two 1

looks_3 2/3

looks_4 4/9

Option looks_two 1

Question no. 11

If z₁ and z₂ are the two complex number then , |z₁ + z₂|

looks_one <=|z₁| + |z₂|

looks_two <=|z₁| - |z₂|

looks_3 <|z₁| + |z₂|

looks_4 >|z₁| + |z₂|

Option looks_one <=|z₁| + |z₂|

For any complex number
|z₁ + z₂| <=|z₁| + |z₂| is true

Question no. 12

If -1+ √-3 = re^iθ , then θ is equal to

looks_one π/3

looks_two -π/3

looks_3 2π/3

looks_4 -2π/3

Option looks_3 2π/3

Question no. 13

If then (x²+y²)²=

looks_one

looks_two

looks_3

looks_4

Option looks_one

Question no. 14

=

looks_one cosnθ - isin nθ

looks_two cosnθ + isin nθ

looks_3 sin nθ + icosnθ

looks_4 sin nθ -icosnθ

Option looks_two cosnθ + isin nθ

Question no. 15

The value of i^1/3 is

looks_one (√3 + i)/2

looks_two (√3 - i)/2

looks_3(1 + √3i)/2

looks_4 (1 - √3i)/2

Option looks_one (√3 + i)/2

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