a straight line through point -a

Let Z 1 and Z 2 be two distinct complex numbers and Z = (1 - t)Z 1 + tZ 2 for some real number t with 0 < t < 1. If arg (w) denotes the principal argument of a non - zero complex number w, then

|Z1 - Z2| + |Z - Z2| = |Z1 - Z2|

A = 2, 3 , B = 1, 5 C = 2, 3, 4, 5

A = 1, B = 2, 3 C = 1, 2 D = 3, 4, 5

A = 2, 3 B = 1, 2, 3 C = 2, 3, 4 D = 1, 2, 5

JEE Questions for Maths Complex Numbers Quiz 4

The complex number z = x + iy which satisfies the equation
Maths-Complex Numbers-14787.png

0%
the X-axis
0%
the straight line y = 3
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a circle passing through origin
0%
None of the above

If the complex numbers z₁, z₂ and z₂ denote the vertices of an isosceles right angled triangle, right angled at z ₁, then(z₁ - z₂)² + (z₁ - z₃) ² is equal to

0%
0
0%
(z2 + z3)2
0%
2
0%
3
0%
(z2 - z3)2

If z₁ and z₂ are two fixed complex numbers in the argand plane, and z is an arbitrary point satisfying |z - z₁|+ |z - z₃| = 2|z₁ - z₂|. Then, the locus of z will

0%
an ellipse
0%
a straight line joining z1 and z2
0%
a parabola
0%
a bisector of the line segment joining z1 and z2

If z₁ is a fixed point on the circle of radius 1 centred at the origin in the argand plane and z₁ ≠ ± 1. Consider an equilateral triangle inscribed in the circle with z₁,z₂, z₃ as the vertices taken in the counter clockwise direction. Then, z₂ z₃ is equal to

0%
z1 2
0%
z1 3
0%
z1 4
0%
z1

Suppose that z₁, z₂ , z₃ are three vertices of an equilateral 1 triangle in the argand plane. If α = 1/2(√3 - i) and β be a non-zero complex number. Then, the points α z₁ +β, αz₂ +β, αz₃ + β will be

0%
the vertices of an equilateral triangle
0%
the vertices of an isosceles triangle
0%
collinear
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the vertices of a scalene triangle

If z is any complex number satisfying |z - 3 - 2i | ≤ 2, then the minimum value of |2z - 6 + 5i|is

0%
2
0%
1
0%
3
0%
5

If z₁ and z₂ are two roots of the equation z₂ + az + b= 0, z being complex number. Further assume that the origin, z₁ and z₂ form an equilateral triangle. Then

0%
a2 = b
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a2 = 2b
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a2 = 3b
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a2 = 4b

If α and β are the roots of x² — 6x — 2 = 0, with α > β and a_n =αⁿ - βⁿ n for n ≥ 1, then the value of
Maths-Complex Numbers-14795.png

0%
1
0%
2
0%
3
0%
4

If z = x + iy is a complex number where x and y are integers. Then, the area of the rectangle whose vertices are the roots of the equation
Maths-Complex Numbers-14797.png

0%
48
0%
32
0%
40
0%
80

If the area of triangle on the argand plane formed by the complex numbers -z, iz, z - iz is 600 sq units, then |z| is equal to

0%
10
0%
20
0%
30
0%
40

If P is the point in the argand diagram corresponding to the complex number √3 + i and if OPQ is an isosceles right angled triangle, right angled at 0, then Q represents the complex number

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- 1 + i √3 or 1 - √3
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1± i√3
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√3 -1 or 1 - i√3
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- 1 ± i√3

The center of a regular hexagon is at the point z = i. If one of its vertices is at 2 + i, then the adjacent vertices of 2 + i are at the points

0%
1 ± 2i
0%
i + 1 ± √3
0%
2 + i(1±√3 )
0%
1 + i (1±√3)
0%
1 - i(1±√3 )

0%
a finite set
0%
an infinite set
0%
an empty set
0%
none of these

0%
an ellipse
0%
a parabola
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a circle
0%
a straight line through point -a

The points representing complex number z for which |z — 3| = |z — 5| lie on the locus given by

0%
an ellipse
0%
a circle
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a straight line
0%
None of these

For three complex numbers 1- i, i, l + i which of the following is correct ?

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They form a right angled triangle
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They are collinear
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They form an equilateral triangle
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They form an isosceles triangle

. Let z₁ , z₂ and z₃ be the affixes of the vertices of a triangle having the circumcentre at the origin. If z is the affix of its orthocentre, then z is equal to

0%
0%
2)
0%
0%
None of these

The points representing the complex numbers z, for which |z - a²| + |z + a|² = b² lie on

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a straight line
0%
a circle
0%
a parabola
0%
a hyberbola

The equation of the locus of z such that
Maths-Complex Numbers-14813.png

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3x2 + 3y2 + 10y - 3 = 0
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3x2 + 3y2 + 10y + 3 = 0
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3x2 - 3y2 + 10y - 3 = 0
0%
x2 + y2 - 5y + 3 = 0

If |z + 4| ≤ 3, then the maximum value of |z + 1|is

0%
4
0%
10
0%
6
0%
0

For all complex numbers z₁, z₂ satisfying |z₁|= 12 and |z₂ - 3 - 4i| = 5, the minimum value of |z₁ - z₂|is

0%
4
0%
3
0%
1
0%
2

0%
2/√21
0%
1/√21
0%
√3
0%
√21

0%
a parabola
0%
a straight line
0%
a circle
0%
an ellipse

The radius of the circle
Maths-Complex Numbers-14821.png

0%
13/12
0%
5/12
0%
5
0%
625

The points z₁, z₂, z₃ and z₄ in the complex plane are the vertices of a parallelogram taken in order, iff

0%
z1 + z4 = z2 + z3
0%
z1 + z3 = z2 + z4
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z1 + z2 = z3 + z4
0%
None of the above

0%
3
0%
4
0%
5
0%
6

0%
i
0%
-i
0%
0%

0%
1
0%
-1
0%
2
0%
-2

0%
0%
2)
0%
0%

Let Z₁ and Z₂ be two distinct complex numbers and Z = (1 - t)Z₁ + tZ₂ for some real number t with 0 < t < 1. If arg (w) denotes the principal argument of a non - zero complex number w, then

0%
|Z1 - Z2| + |Z - Z2| = |Z1 - Z2|
0%
arg (Z - Z= arg (Z - Z2)
0%
0%
All of these

0%
A = 2, 3 , B = 1, 5 C = 2, 3, 4, 5
0%
A = 1, B = 2, 3 C = 1, 2 D = 3, 4, 5
0%
A = 2, 3 B = 1, 2, 3 C = 2, 3, 4 D = 1, 2, 5
0%
None of the above

Which of the following statement(s) is/are false

0%
0%
2)
0%
0%
none of these

0%
0%
2)
0%
0%
none of these

If arg(z) < 0, then arg(−z) − arg z =

0%
π
0%
− π
0%
0%

If z₁ and z₂ be the nth roots of unity which subtend right angle at the origin. Then n must be of the form

0%
4 k + 1
0%
4 k + 2
0%
4 k + 3
0%
4 k

Length of the line segment joining the points –1 –i and 2 + 3i is

0%
–5
0%
15
0%
5
0%
25

0%
0%
2)
0%
0%
None of these

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

0%
4
0%
10
0%
6
0%
0

If |z| = 2, then the points representing the complex numbers -1+ 5z will lie on a

0%
Circle
0%
Straight line
0%
Parabola
0%
None of these

In the Argand plane, the vector z = 4 – 3i is turned in the clockwise sense through 180^o and stretched three times. The complex number represented by the new vector is