JEE Questions for Maths Complex Numbers Quiz 2 - MCQExams.com


Maths-Complex Numbers-14566.png
  • Re(z) = 0
  • Im(z) = 0
  • Re(z) > 0, Im (z) > 0
  • Re(z) > 0, Im (z) < 0
If 2α = 1- i√3 and 2β = -1 + i√3, then 5α4 + 5β4 + 7α-1β-1 is equal to
  • -1
  • -2
  • 0
  • 1
  • 2
If an = i (n+1)2, where i =√-1 and n = 1,2,3... Then , the value of a1 + a3 +a5+...+a25 is
  • 13
  • 13 + i
  • 13 - i
  • 12
  • 12 - i
Let
Maths-Complex Numbers-14570.png
  • 4
  • -4
  • 7
  • -7
The value of sum
Maths-Complex Numbers-14572.png
  • i
  • i -1
  • - i
  • 0
If z = x - iy and z1/3 = p + iq, then
Maths-Complex Numbers-14574.png
  • 1
  • -1
  • 2
  • -2

Maths-Complex Numbers-14576.png

  • Maths-Complex Numbers-14577.png
  • 2)
    Maths-Complex Numbers-14578.png

  • Maths-Complex Numbers-14579.png

  • Maths-Complex Numbers-14580.png
If z is a complex number such that Re(z) = Im(z), then
  • Re (z= 0
  • Im (z= 0
  • Re (z= Im(z2)
  • Re (z= -Im(z2)
  • z2 = 0
If z is a complex number of unit modulus and argument θ, then
Maths-Complex Numbers-14583.png
  • - θ
  • 2)
    Maths-Complex Numbers-14584.png
  • θ
  • π - θ
If α and β are two different complex numbers with |β| = 1, then
Maths-Complex Numbers-14586.png
  • 1/2
  • 0
  • -1
  • 1
Let w ≠ ± 1 be a complex number. If |w|= land
Maths-Complex Numbers-14588.png
  • 1
  • 2)
    Maths-Complex Numbers-14589.png
  • Re (ω)
  • 0
  • ω + ω

Maths-Complex Numbers-14591.png

  • Maths-Complex Numbers-14592.png
  • 2)
    Maths-Complex Numbers-14593.png

  • Maths-Complex Numbers-14594.png

  • Maths-Complex Numbers-14595.png
If z1 and z2 are two complex numbers such that |z1| = |z2| + |z1 - z2|, then

  • Maths-Complex Numbers-14597.png
  • 2)
    Maths-Complex Numbers-14598.png

  • Maths-Complex Numbers-14599.png
  • None of these
If the conjugate of (x + iy) (1 - 2i) is 1 + i, then

  • Maths-Complex Numbers-14601.png
  • 2)
    Maths-Complex Numbers-14602.png

  • Maths-Complex Numbers-14603.png

  • Maths-Complex Numbers-14604.png
If
Maths-Complex Numbers-14606.png
  • 6
  • √2
  • √6
  • √3
  • √2 + √3
If z = r (cos θ + i sin θ), then the value of
Maths-Complex Numbers-14608.png
  • cos 2θ
  • 2cos 2θ
  • 2cos θ
  • 2 sin θ
  • 2 sin 2θ

Maths-Complex Numbers-14610.png
  • ω
  • -ω

  • Maths-Complex Numbers-14611.png

  • Maths-Complex Numbers-14612.png

Maths-Complex Numbers-14614.png
  • √3 + 1
  • √5 + 1
  • 2
  • 2 + √2
If z = √3 + i, then the argument of Z2 ez-1 i is equal to

  • Maths-Complex Numbers-14616.png
  • 2)
    Maths-Complex Numbers-14617.png

  • Maths-Complex Numbers-14618.png

  • Maths-Complex Numbers-14619.png

  • Maths-Complex Numbers-14620.png
For any complex number Z, the minimum value of |Z| + |Z - 1| is
  • 0
  • 1
  • 2
  • -1
The solution of equation |Z| - Z = 1 + 2i is

  • Maths-Complex Numbers-14623.png
  • 2)
    Maths-Complex Numbers-14624.png
  • 3 - 2i
  • None of these
The modulus of
Maths-Complex Numbers-14626.png

  • Maths-Complex Numbers-14627.png
  • 2)
    Maths-Complex Numbers-14628.png

  • Maths-Complex Numbers-14629.png

  • Maths-Complex Numbers-14630.png

Maths-Complex Numbers-14632.png

  • Maths-Complex Numbers-14633.png
  • 2)
    Maths-Complex Numbers-14634.png

  • Maths-Complex Numbers-14635.png
  • None of these
The amplitude of
Maths-Complex Numbers-14637.png

  • Maths-Complex Numbers-14638.png
  • 2)
    Maths-Complex Numbers-14639.png

  • Maths-Complex Numbers-14640.png

  • Maths-Complex Numbers-14641.png

Maths-Complex Numbers-14643.png
  • |Z1 + Z2|
  • |Z1 - Z2|
  • |Z1| +| Z2|
  • |Z1| -| Z2|
The conjugate of the complex number
Maths-Complex Numbers-14645.png
  • 1 - i
  • 1 + i
  • -1 + i
  • -1 - i
If z is a complex number such that z = - ¯z, then
  • z is purely real
  • z is purely imaginary
  • z is any complex number
  • real part of z is same as its imaginary part

Maths-Complex Numbers-14648.png

  • Maths-Complex Numbers-14649.png
  • 2
  • 1
  • 3

  • Maths-Complex Numbers-14650.png

Maths-Complex Numbers-15019.png

  • Maths-Complex Numbers-15020.png
  • 2)
    Maths-Complex Numbers-15021.png

  • Maths-Complex Numbers-15022.png

  • Maths-Complex Numbers-15023.png
A and B are two points on the argand plane such that the segment AB is bisected at the point (0, 0). If the point A, which is in the third quadrant has principal amplitude θ, then the principal amplitude of the point B is
  • -θ
  • π - θ
  • θ - π
  • π + θ
For two complex numbers z1, z2, the relation |z1 + z2 |= |z1 |+ |z2| holds , if
  • arg(z= arg(z2)
  • 2)
    Maths-Complex Numbers-14653.png
  • Z1Z2 = 1
  • |z1| = |z2|
The complex number
Maths-Complex Numbers-14655.png
  • in the second quadrant
  • in the first quadrant
  • on the Y-axis (imaginary axis)
  • on the X-axis (real axis)
The magnitude and amplitude of
Maths-Complex Numbers-14657.png

  • Maths-Complex Numbers-14658.png
  • 2)
    Maths-Complex Numbers-14659.png

  • Maths-Complex Numbers-14660.png

  • Maths-Complex Numbers-14661.png
For any two complex numbers Z1 and Z2 and any real numbers a and b, |(az1 - bz2)|2+ |(bz1 + az2)|2 is equal to
  • (a 2+ b(|z1| + |z2|)
  • (a2 + b(|z1| + |z2|2)
  • (a2 + b(|z1| - |z2|2)
  • None of these
The complex numbers sin x + i cos 2x and cos x - i sin 2x are conjugate to each other for
  • x = n π
  • 2)
    Maths-Complex Numbers-14664.png
  • x = 0
  • no value of x
The number of non - zero integral solutions of the equation |1 - i|x = 2x is
  • infinite
  • 1
  • 2
  • None of these
If arg (z) = θ , then arg(¯z) is equal to
  • θ - π
  • π - θ
  • θ
  • - θ
If z and ω be complex numbers such that ¯z + iω = 0 and arg(zω) = π. Then, arg (z) equals

  • Maths-Complex Numbers-14668.png
  • 2)
    Maths-Complex Numbers-14669.png

  • Maths-Complex Numbers-14670.png

  • Maths-Complex Numbers-14671.png

Maths-Complex Numbers-14673.png
  • 1
  • 2
  • 3
  • 4
If If ω = α + iβ, (where β ≠ 0 and z # 1, satisfies the ). condition that
Maths-Complex Numbers-14675.png
  • |z| = 1, z ≠ 2
  • |z| = 1 and z ≠ 1
  • Z = ¯z
  • None of these
The modulus and amplitude of
Maths-Complex Numbers-14677.png

  • Maths-Complex Numbers-14678.png
  • 1 and 0

  • Maths-Complex Numbers-14679.png

  • Maths-Complex Numbers-14680.png
If z1 and z2 be complex numbers, then |z1 + z2|2+ |z1 - z2|2 equal to
  • |z1|2 + |z2|2
  • 2(|z1|2 + |z2|2)
  • 2(z1 + z2)2
  • 4 z1 z2
If z1 and z2 are any two complex numbers, then
  • |z1 + z2| ≥ |z1|+ |z2|
  • |z1 + z2| > |z1|+|z2|
  • |z1 + z2| ≤ |z1|+|z2|
  • |z1 + z2| = |z1|+|z2|
The arrange of
Maths-Complex Numbers-14684.png

  • Maths-Complex Numbers-14685.png
  • 2)
    Maths-Complex Numbers-14686.png

  • Maths-Complex Numbers-14687.png

  • Maths-Complex Numbers-14688.png
The number of solutions for the equations |z - 1| = |z - 2| = |z - i| is
  • 1 solution
  • 3 solutions
  • 2 solutions
  • no solution

Maths-Complex Numbers-14691.png
  • a(3 - i), a ϵ R
  • 2)
    Maths-Complex Numbers-14692.png
  • a(3 + i), a ϵ R
  • a(-3 + i), a ϵ R
If z1 = 1 + 2i and z2 = 3 + 5i, then Re[¯z2 z1 /z2]

  • Maths-Complex Numbers-14694.png
  • 2)
    Maths-Complex Numbers-14695.png

  • Maths-Complex Numbers-14696.png

  • Maths-Complex Numbers-14697.png
If z = e(2πi/3), then 1+ z + 3z2 +2z3 +2z4 +3z5 is equal to
  • - 3e(2πi/3)
  • 3e(πi/3)
  • 3e(πi/3)
  • - 3e(2πi/3)
  • 0
If ω and ω2 are the cube roots of unity, then roots of equation (x - 1)3 + 5 = 0 are
  • - 5, -5ω, - 5ω2
  • )- 4,1- 5ω,1- 5ω2
  • 6,1- 5ω,1 + 5ω2
  • None of these
If (√3i + 1)100 =299 (a + ib), then a2 + b2 is equal to
  • 4
  • 3
  • 2
  • 0
0:0:1


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