Line segment joining of point 2 + 3i and -2 + 6i

z1, z2 and the origin from an equilateral triangle

z1, z2 and the origin form a right angled triangle

A circle passing through the origin

Interior and boundary of an ellipse

JEE Questions for Maths Complex Numbers Quiz 14

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(2,0)
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2)
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(4,0)

If z = x + iy , then area of the triangle whose vertices are points z, iz and z + zi is

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2|z|2
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2)
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|z|2
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If z₁ and z₂ are two complex numbers, then |z₁ + z₂| is

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2)
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An ellipse
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ϕ
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Line segment joining of point 2 + 3i and -2 + 6i
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None of these

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2)
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If z₁, z₂, z₃ are affixes of the vertices A,B and C respectively of a triangle ABC having centroid at G such that z = 0 is the mid point of AG, then

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z1 + z2 + z3 = 0
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z1 + 4z2 + z3 = 0
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z1 + z2 + 4z3 = 0
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4z1 + z2 + z3 = 0

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z1, z2 are collinear
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z1, z2 and the origin form a right angled triangle
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z1, z2 and the origin from an equilateral triangle
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None of these

If the area of the triangle formed by the points z, z + iz and iz on the complex plane is 18, then the value of |z| is

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6
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9
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3√2
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2√3

Which one of the following statement is true

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2)
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The area of triangle whose vertices are represented by the complex numbers 0, z, ze^iα, (0 < α < π) equals

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2)
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If z₁ = 1 + 2i, z₂ = 2 + 3i, z₃ = 3 + 4i, then z₁, z₂, z₃ represents the vertices of a / an

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Equilateral triangle
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Isosceles triangle
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Right angled triangle
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None of these

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Real axis
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The line y = 5
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A circle passing through the origin
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None of these

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2)
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Straight line
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Parabola

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x - axis
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y - axis
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The straight line x = a
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None of these

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Interior of an ellipse
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Exterior of a circle
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Interior and boundary of an ellipse
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None of the above

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A straight line
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A circle
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A parabola
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None of these

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A circle
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A straight line
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A parabola
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None of these

If z = x + iy and |z - zi| = 1, then

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z lies on x - axis
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z lies on y - axis
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z lies on a circle
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None of these

R(z²) = 1 is represented by

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The parabola x2 + y2 = 1
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The hyperbola x2 - y2 = 1
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Parabola or a circle
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All the above

The locus represented by |z - 1| = |z + i| is

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A circle of radius 1
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An ellipse with foci at (1,, and (0, -1)
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A straight line through the origin
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A circle on the line joining (1,0), (0,as diameter

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|z| = 5
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|z| < 5
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|z| > 5
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None of these

Locus of the point z satisfying the equation |iz - 1| + |z - i| = 2 is

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A straight line
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A circle
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An ellipse
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A pair of straight lines

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2y = x
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y = x
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y-axis
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x-axis

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Fourth quadrant
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First quadrant
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Second quadrant
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Third quadrant

If the amplitude of z – 2 – 3i is π/4, then the locus of z = x + iy is

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x + y – 1 = 0
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x – y – 1 = 0
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x + y + 1 = 0
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x – y + 1 = 0

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z will be at imaginary axis
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z will be at real axis
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z will be at unity circle
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None of the above

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A straight line
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A circle
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A parabola
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An ellipse

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A straight line
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A parabola
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An ellipse
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A circle

If |8 + z| + |z - 8| = 16, where z is a complex number, then the point z will lie on

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A circle
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An ellipse
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A straight line
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None of the above

Which of the following equations can represent a triangle

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|z – 1| = |z – 2|
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|z – 1| = |z – 2| = |z – i|
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|z – 1| – |z – 2| = 2a
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|z – 1|2 + |z – 2|2 = 4

The points representing the complex number z, for which |z – a|² + |z + a|² = b² lie on

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A straight line
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A circle
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A parabola
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A hyperbola

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 principle amplitude 0, then the principle amplitude of the point B is

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– θ
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π – θ
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θ – π
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π + θ

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Circle
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Pair of lines
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Parabola
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Hyperbola

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A finite set
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An infinite set
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An empty set
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None of these

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An ellipse
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A parabola
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A circle
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A hyperbola

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Hyperbola
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Ellipse
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Circle
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Straight line

A(z₁), B(z₂) and C(z₃) be the vertices of an equilateral triangle in the argand plane such that |z₁| = |z₂| = |z₃|. Then which of the following is false ?