question 1

If (ω ≠ 1) be a cube root of unity and (1 + ω)^{7}
= A + Bω, then A and B are respectively the numbers

- 0, 0
- 0, 1
- 1, 1
- 1, 0
- - 1, 1

question 2

If ω (≠ 1) is a cube root of unity, then equals

- 0
- 1
- i
- ω
- none of these

question 3

Let z and w be two non-zero complex numbers such that | z | = | w | and arg (z) + arg (w) = π. Then z equals

- w
- - w
- -
- none of these

question 4

The smallest positive integer n for which (1 + i)^{2n} = (1 - i)^{2n} is

- 4
- 8
- 2
- 12
- none of these

question 5

The complex number [(1 + 2i) ⁄ (1 - i)] lies in

- I
^{ st}quadrant - II
^{ nd}quadrant - III
^{ rd}quadrant - IV
^{ th}quadrant - cannot be determined

question 6

If α and β are different complex numbers with | β | = 1, then is

- 0
- ½
- 1
- 2
- none of these

question 7

If z_{1}, z_{2}, z_{3}
are vertices of an equilateral triangle inscribed in a circle | z | = 2 and if z_{1}
= 1 + i√3, then

- z
_{2}= -2, z_{3}= 1 - i√3 - z
_{2}= 2, z_{3}= 1 - i√3 - z
_{2}= -2, z_{3}= - 1 - i√3 - z
_{2}= 1 - i√3, z_{3}= - 1 - i√3 - none of these

question 8

The value of the expression 1.(2 - ω)(2 - ω²) + 2.(3 - ω)(3 - ω²) + ... + (n - 1)(n - ω)(n - ω²), where ω is an imaginary cube root of unity is

- 1
- 0

syllabus

Complex Numbers – Introduction; Iota (*i*), Powers of Iota (*i*),
Imaginary Quantities; Equality of Complex Numbers; Addition, Subtraction,
Multiplication and Division of Complex Numbers; Properties of Addition,
Subtraction, Multiplication and Division of Complex Numbers; Conjugate, Modulus,
Reciprocal (Inverse) and Square Root of a Complex Number; Properties of
Conjugate, Properties of Modulus; Cube Roots of Unity, Properties of Cube Roots
of Unity, Sum of Cube Roots of Unity, Product of Cube Roots of Unity;
Representations of Complex Number – Geometrical Form, Vectorial Form and
Trigonometrical Form or Polar Form; Geometrical Representation of Complex
Number; Argument or Amplitude of a Complex Number; Modulus of a Complex Number;
Geometrical Representations of Fundamental Operations – Geometrical
Representation of Addition, Subtraction, Multiplication, Division and Conjugate
of Complex Numbers; Multiplication of a Complex Number by Iota(*i*);
Results on Modulus and Argument; Distance between Points, Affix of Point,
Equation of Circle; De-Moivre's Theorem; Extraction of Roots of a Complex
Number, n^{th} roots of Complex Number, n^{th}
roots of Unity, Properties of n^{th} roots of Unity.