JEE Questions for Maths Complex Numbers Quiz 1 - MCQExams.com


Maths-Complex Numbers-14464.png
  • n = 8
  • n = 16
  • n = 12
  • none of these

Maths-Complex Numbers-14466.png

  • Maths-Complex Numbers-14467.png
  • 2)
    Maths-Complex Numbers-14468.png

  • Maths-Complex Numbers-14469.png
  • none of these

Maths-Complex Numbers-14470.png
  • z lies on the imaginary axis
  • z lies on the real axis
  • z lies on the unit circle
  • None of these
The points z1, z2, z3 z4 in the complex plane are the vertices of a parallelogram taken in order if and only if
  • z1 + z4 = z2 + z3
  • z1 + z3 = z2 + z4
  • z1 + z2 = z3 + z4
  • None of these
The smallest positive integer n for which (1+ i)2n = (1 - i)2n is
  • 1
  • 2
  • 3
  • 4
The values of x and y satisfying the equation
Maths-Complex Numbers-14473.png
  • x = -1, y = 3
  • x = 3 y = -1
  • x = -0, y = 1
  • x = 1, y = 0
Let z1 ≠ z2 and |z1| = |z2|.If z1 has positive real part and z2 has negative imaginary part. Then,
Maths-Complex Numbers-14475.png
  • 0
  • real and positive
  • real and negative
  • None of the above

Maths-Complex Numbers-14477.png
  • 8
  • 2
  • 5
  • 4
  • 10
If z(2- i2√3)2 = i(√3 + i)4, then amplitude of z is

  • Maths-Complex Numbers-14479.png
  • 2)
    Maths-Complex Numbers-14480.png

  • Maths-Complex Numbers-14481.png
  • None of these
If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c = (1 – r) a + rb and w = (1 – r)u + rv, where r is a complex number, then the two triangles
  • have the same area
  • are similar
  • are congruent
  • none of these
If|z1 + z2|2 = |z1|2 + |z2|2 , then z1/z2 is
  • purely real
  • purely imaginary
  • zero of purely imaginary
  • Neither real nor imaginary

Maths-Complex Numbers-14485.png
  • 0, 1
  • 1, 1
  • 1, 0
  • – 1, 1
If Z1 are Z2 two non - zero complex numbers such that |Z1 + Z2|= |Z1||Z2|, then
Maths-Complex Numbers-14487.png
  • 0
  • -π

  • Maths-Complex Numbers-14488.png

  • Maths-Complex Numbers-14489.png
  • π

Maths-Complex Numbers-14491.png
  • 2(1 + i)
  • (1 + i)

  • Maths-Complex Numbers-14492.png

  • Maths-Complex Numbers-14493.png

Maths-Complex Numbers-14495.png
  • π
  • -π

  • Maths-Complex Numbers-14496.png

  • Maths-Complex Numbers-14497.png
If z and w are two complex numbers such that |Z| ≤ 1, |W|≤ 1 and |Z + iw| = |Z - i¯w |= 2, Then, z is equal to
  • 1 or i
  • i or - i
  • 1 or - 1
  • i or - 1
The locus of Z satisfying the inequality
Maths-Complex Numbers-14500.png
  • x2 + y2 < 1
  • x2 - y2 < 1
  • x2 + y2 > 1
  • 2x2 + 3y2 < 1
If (3+ i)(z + ¯z) - (2+ i) (z - ¯z) + 14i = 0, then z¯z is equal to
  • 5
  • 8
  • 10
  • 40

Maths-Complex Numbers-14503.png
  • 0
  • 1
  • -1
  • 2
If m1 , m2 , m3 and m4 respectively denote the moduli of the complex numbers 1 + 4i, 3 + i,1- i and 2 - 3i , then the correct one, among the following is
  • m1 < m2 < m3 < m4
  • m4 < m3 < m2 < m1
  • m3 < m2 < m4 < m1
  • m3 < m1 < m2 < m4
The real part of (1 - cosθ + 2 i sinθ) -1 is

  • Maths-Complex Numbers-14506.png
  • 2)
    Maths-Complex Numbers-14507.png

  • Maths-Complex Numbers-14508.png

  • Maths-Complex Numbers-14509.png

Maths-Complex Numbers-14511.png

  • Maths-Complex Numbers-14512.png
  • 6
  • -18
  • 36
One of the values of
Maths-Complex Numbers-14514.png
  • √3 + i
  • - i
  • i
  • -√3 + i

Maths-Complex Numbers-14516.png
  • ±(b + ia)
  • ±(a - ib)
  • (ai + b)
  • ±(b - ia)
  • None of these
The value of
Maths-Complex Numbers-14518.png
  • ω3
  • ω2
  • ω3 - ω
  • ω
In the argand plane, the distinct roots of 1+ z+ z3 + z4 = 0 (z is a complex number) represent vertices of
  • a square
  • an equilateral triangle
  • a rhombus
  • a rectangle
Among the complex number z satisfying condition| z +1 - i| ≤ 1, the number having the least positive argument is
  • 1 - i
  • 1 + i
  • - i
  • none of these

Maths-Complex Numbers-14522.png
  • a circle
  • a square
  • an ellipse
  • a line

Maths-Complex Numbers-14524.png
  • circle
  • pair of lines
  • paraabola
  • hyperbola

Maths-Complex Numbers-14526.png
  • |a|2 = b
  • |a|2 > b
  • |a|2 < b
  • none of these
The region of the argand diagram defined by |z - 1|+ |z + 1| ≤ 4 is an
  • interior of an ellipse
  • exterior of a circle
  • interior and boundary of an ellipse
  • None of the above
If the complex numbers z1, z2, z3 are in an AP, then they lie on
  • a circle
  • a parabola
  • a straight line
  • an ellipse
If |z2 -1| = |z|2 + 1, then z lies on
  • the real axis
  • the imaginary axis
  • a circle
  • an ellipse

Maths-Complex Numbers-14531.png
  • an ellispse
  • a parabola
  • a straight line
  • a circle
The locus of the point z = x + iy satisfying the equation
Maths-Complex Numbers-14533.png
  • x = 0
  • y = 0
  • x = y
  • x + y = 0
If z = x + iy, then area of the triangle whose vertices are points z, iz, z + iz is

  • Maths-Complex Numbers-14535.png
  • 2)
    Maths-Complex Numbers-14536.png

  • Maths-Complex Numbers-14537.png

  • Maths-Complex Numbers-14538.png
If arg (z - a) = π/4, where a ϵ R, then the loss of z ϵ C is a
  • hyperbola
  • parabola
  • ellipse
  • straight line
If the complex numbers z1 , z2 and z3 satisfying
Maths-Complex Numbers-14541.png
  • an equilateral triangle
  • a right angled triangle
  • an acute angled triangle
  • an obtuse angled isosceles triangle
If magnitude of a complex number 4 - 3i is tripled and is rotated anti-clockwise by an angle π, then resulting complex number would be
  • -12 + 9i
  • 12 + 9i
  • 7 - 6i
  • 7 + 6i
If |z + 8| + |z - 8|= 16, where z is a complex number, then the point z will lie on
  • a circle
  • an ellipse
  • a straight line
  • None of the above
The point (4,undergoes the following three transformations successively
I. reflection about the line y= x .
II. translation through a distance of 2 units along the positive direction of X-axis .
III. rotation through an angle of 4 —n about the origin in the anti-clockwise direction
The final position of the point is

  • Maths-Complex Numbers-14545.png
  • 2)
    Maths-Complex Numbers-14546.png
  • (- √2, 7√2)
  • (√2, 7√2)
  • (√2, - 7√2)
The imaginary part of
Maths-Complex Numbers-14548.png
  • 4/5
  • 0
  • 2/5
  • -(4/5)
The product of all values of (cosα + i sinα)3/5 is
  • 1
  • cosα + i sinα
  • cos 3α + i sin 3α
  • cos 5α + i sinα
If |Z1 + Z2| = |Z1| + |Z2|, then find arg Z1 - Z2
  • 0
  • 1
  • -1
  • 2

Maths-Complex Numbers-14551.png
  • 45o
  • 135o
  • 225o
  • 240o

Maths-Complex Numbers-14553.png

  • Maths-Complex Numbers-14554.png
  • 45 + 3i

  • Maths-Complex Numbers-14555.png

  • Maths-Complex Numbers-14556.png
If the cube roots of unity are 1, w, w2, then the roots of the equation (x – 1)3 + 8 = 0 are
  • – 1, 1 + 2w, 1 + 2w2
  • – 1, 1 – 2w, 1 – 2w2
  • – 1, – 1, – 1
  • None of these
If z is a complex number such that the imaginary part of z is non- Zero and a = z2 + z + 1 is real. Then, a cannot take the value
  • -1
  • 2)
    Maths-Complex Numbers-14559.png

  • Maths-Complex Numbers-14560.png

  • Maths-Complex Numbers-14561.png
If 2x = 3 + 5i, then the value of 2x3 + 2x2 - 7x +72 is
  • 4
  • -4
  • 8
  • -8

Maths-Complex Numbers-14564.png
  • the x-axis
  • the straight line y = 5
  • a circle passing through the origin
  • none of these
0:0:1


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