A line not passing through the origin

JEE Questions for Maths Complex Numbers Quiz 13

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0

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0

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0
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Purely imaginary
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Purely real
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None of these

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None of these

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None of these

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The sum of amplitude of z and another complex number is π. The other complex number can be written

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1
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–1
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i
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–i

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9
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3

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6
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–1
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None of these

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2
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1
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4
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3

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–1
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The points z₁, z₂, z₃, z₄ in the complex plane are the vertices of a parallelogram taken in order, if and only if

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z1 + z4 = z2 + z3
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z1 + z3 = z2 + z4
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z1 + z2 = z3 + z4
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None of these

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If three complex number are in A.P., then they lie on

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A circle in the complex plane
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A straight line in the complex plane
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A parabola in the complex plane
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None of the above

If a and b are real numbers between 0 and 1 such that the points z₁ = a + i, z₂ = 1 + bi and z₃ = 0 form an equilateral triangle ,then

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None of these

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48
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32
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40
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80

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A line not passing through the origin
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The x-axis
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The y-axis

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The vertices B and D of a parallelogram are 1 - 2i and 4 + 2i. If the diagonals are at right angles and AC = 2BD, the complex number representing A is

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3i - 4
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3i + 4

ABCD is a rhombus . Its diagonals AC and BD intersect at the point M and satisfy BD = 2AC. If points D and M respectively. then A represents the complex number

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None of these

The complex nu,mbers z₁, z₂, z₃ are the vertices of a triangle. Then, the complex numbers z which make the triangle into a parallelogram is

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z1 + z2 – z3
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z1 – z2 + z3
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z2 + z3 – z1
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All of these

A rectangle is constructed in the complex plane with its sides parallel to the axes and its centre is situated as the origin. If one of the vertices of the rectangle is a +ib√3, then the area of the rectangle is

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If the points P₁ and P₂ represents two complex numbers z₁ and z₂, then the point P₃ represents the number
Maths-Complex Numbers-16757.png

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z1 + z2
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z1 – z2
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z1 × z2
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z1 ÷ z2

If complex numbers z₁, z₂ and z₃ represents the vertices A,B and C respectively of an isosceles triangle ABC of which ∠C is right angle, then correct statement is