Complex Numbers

1. x = 1 and y =2
2. x = 2 and y =1
3. x = 2 and y =2
4. x = 1 and y =1
The polar form of a complex number is
1. r ( tanθ + icotθ )
2. r(secθ + icosecθ )
3. r(cosθ + isinθ )
4. r (sinθ + icosθ)
|z1 + z2 | =
1. > |Z1| + |Z2|
2. ≤|Z1| + |Z2|
3. ≤ Z1 + Z2
4. > Z1 + Z2
|z1 - z2 | =
1. > |Z1| + |Z2|
2. ≤|Z1| + |Z2|
3. ≤ Z1 + Z2
4. > Z1 + Z2
Number of solutions to the equation (1 –i)^x = 2^x is :
1. 1
2. 2
3. 3
4. None
If , arg(z) < 0, then arg(-z) - arg(z) =
1. π
2. –π/4
3. –π/2
4. π/2
If ω is an imaginary cube root of unity, then (1 + ω – ω²)⁷ equals :
1. 128 ω
2. 128 ω²
3. -128 ω
4. -128 ω²
Value of ω¹⁹⁹⁹ + ω²⁹⁹ + 1 is
1. 0
2. 1
3. --1
4. 2
Principal argument of z = -√3+i is :
1. 5π/6
2. π/6
3. -5π/6
4. None
Which one is not a root of the fourth root of unity.
1. i
2. 1
3. i/√2
4. -i
If z³ – 2z² + 4z – 8 = 0 then
1. ∣z∣=1
2. ∣z∣=2
3. ∣z∣=3
4. None
i¹ + i² + i³ + i⁴ + ……… + i¹⁰⁰⁰ =
1. 0
2. 1
3. -1
4. None
The small positive integer ‘n’ for which (1+i)²ⁿ = (1-i)²ⁿ is :
1. 2
2. 4
3. 8
4. 12
The inequality | z – 4| < |z – 2| represents the region given by
1. Re (z) ≥ 0
2. R (z) < 0
3. Re (z) > 0
4. None
If z = x + iy and w = (1 – iz) / (z – i), then |w| = 1 implies that, in the complex plane
1. z lies on the imaginary
2. z lie on the real axis
3. z lies on the unit circle
4. None
The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order, if and only if
1. z1 + z4 = z2 + z3
2. z1 + z3 = z2 + z4
3. z1 + z2 = z3 + z4
4. None
If a, b, c and u, v, w are the 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
1. Have the same area
2. Are similar
3. Are congruent
4. None
If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2|, then arg (z1) – arg (z2) is equal to
1. – π
2. -π/2
3. 0
4. i
The complex numbers sin x + i cos 2x and cos x – i sin 2x are conjugate to each to other, for
1. x = nπ
2. x = 0
3. x = (n + 1/2)π
4. No value of x
If z and w are two nonzero complex numbers such that ∣zw∣=1 and arg z−arg w= π/2 then zˉw is equal to
1. -1
2. i
3. -i
4. 1

Complex Numbers

Quiz