Complex Numbers

Question 1

Iota(i) is equal to

Answer 1

root(-1)

Question 2

How is a complex number defined?

Answer 2

z = a+ib, where a and b both are real

Question 3

Purely Real, Purely Imaginary, Imaginary

Answer 3

Purely real - b=0
Purely Imaginary - a=0
Imaginary - b is not equal to 0

Question 4

The real part and Imaginary part of complex number

Answer 4

x and y

Question 5

i^4k, 4k+1, 4k+2, 4k+3

Answer 5

1, i, (-1), -i

Question 6

Sum of four consecutive integral power of i is

Answer 6

0

Question 7

Conjugate of x+iy is

Answer 7

x-iy

Question 8

z+z’ =

Answer 8

2*Real(z)

Question 9

z-z’ =

Answer 9

2*Imaginary(z)

Question 10

Modulus of a complex number |z|

Answer 10

|z| = root(Re(z)^2 + Im(z)^2)

Question 11

z*z’

Answer 11

|z|^2

Question 12

Locus of |z-z1|=|z-z2|

Answer 12

It is the perpendicular bisector of z1z2

Question 13

Locus of |z-zo|=r

Answer 13

It is a circle with a centre zo and radius r

Question 14

Amplitude/Argument (phi) of a complex number

Answer 14

|y|/|x|
The complex number has infinite arguments.

Question 15

Cartesian Form or Algebraic Form

Answer 15

z = x+iy

Question 16

Trigonometric Form or Polar Form

Answer 16

z = |z|cisθ

Question 17

Euler’s Form

Answer 17

z = |z|e^iθ

Question 18

|z-z1| is

Answer 18

Distance between z and z1

Question 19

Angle between lines

Answer 19

θ = arg(Final vector)/(Initial Vector)

Question 20

Complex Slope

Answer 20

z2-z1/z2’-z1’

Question 21

1/w

Answer 21

w^2

Question 22

Cyclicity of w

Answer 22

w^3k = 1
w^3k+1 = w
w^3k+2 = w^2

Question 23

a^3-b^3 defined in terms of w and w^2

Answer 23

(a-b)(a-bw)(a-bw^2)

Question 24

a^3+b^3 defined in terms of w and w^2

Answer 24

(a+b)(a+bw)(a+bw^2)

Question 25

a^3+b^3+c^3-3abc

Answer 25

(a+b+c)(a+bw+cw^2)(a+bw^2+cw)