Complex Numbers Test

Result

Complex Numbers Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

If (-1 + √ 3i)ⁿ+ (-1 - √ 3i)ⁿ= 2ⁿ, then is equal to

A
2

B
-1

C
2 or -1

D
None of these
Question 2
1 / -0

The complex numbers z = x + y i which satisfy the equation = 1 lie on

A
the X-axis

B
the straight line y = 3

C
a circle passing through the origin

D
the Y-axis
Question 3
1 / -0

If k, l, m, n are four consecutive integers, then jk + jl + jm + jn is equal to

A
1

B
0

C
2

D
4
Question 4
1 / -0

If x = , then x³ equals

A
1

B
-1

C
i

D
- i
Question 5
1 / -0

Find the value of (1 + )⁴.

A
³

B
²

C

D
None of these
Question 6
1 / -0

If │z│= 1, then z - 1/(z + 1), z ≠ -1 is

A
purely real

B
non-real

C
purely imaginary or zero

D
None of these
Question 7
1 / -0

If w is cube root of unity, then ( 1 + w) ( 1 + w²) ( 1 + w⁴) ( 1 + w⁸)… upto 2n factors is

A
1

B
-1

C
0

D
None of these
Question 8
1 / -0

If w is a non real cube root of unity and (1+ w)⁹ = a + b w; a, b R, then a and b are respectively the numbers

A
0, 1

B
1, 0

C
-1, 0

D
0, -1
Question 9
1 / -0

Let x, y R, then x + yi is a non- real complex number if

A
x = 0

B
y = 0

C
x ≠ 0

D
y ≠ 0
Question 10
1 / -0

The inequality │z - 4│< │z - 2│represents the region given by

A
Re(z) > 0

B
Re(z) < 0

C
Re(z) > 2

D
None of these
Question 11
1 / -0

z + z` ≠ 0 if and only if

A
Re(z) ≠ 0

B
Im (z) ≠ 0

C
z ≠ 0

D
│z│≠ 0
Question 12
1 / -0

Multiplicative inverse of the non- zero complex number x + yi (x, y R) is

A
x/(x + y) - y/(x + y) i

B
x/(x²+ y²) - y/(x²+ y²) i

C
-x/ (x²+ y²) + y/ (x²+ y²) i

D
x/(x + y) + y/(x + y) i
Question 13
1 / -0

Locus of z = 2 + i Im (z) is given by

A
a circle

B
a straight line parallel to x - axis

C
a straight line parallel to y - axis

D
None of these
Question 14
1 / -0

i² + i⁴ + i⁶ +…. Upto 2 k + 1 terms, k ª N, is

A
0

B
1

C
-1

D
none of these
Question 15
1 / -0

If (x + yi) (3 - 4i) = 5 + 12i, then √ (X²+ y²) =

A
65

B
513

C
135

D
18
Question 16
1 / -0

2 √ -9 √ -16, is equals to

A
24

B
-24

C
48

D
- 48
Question 17
1 / -0

Let x, y R, then x + yi is a purely imaginary number if

A
x = 0, y ≠ 0

B
x ≠ 0, y = 0

C
x ≠ 0, y ≠ 0

D
x = 0, y = 0
Question 18
1 / -0

The inequality │z - 6│< │z - 2│represents the region given by

A
Re(z) > 4

B
Re(z) < 0

C
Re(z) > 2

D
Re(z) > 3
Question 19
1 / -0

If (√ 3 + i )¹⁰ = a + bi ; a, b ª R, then a and b are respectively

A
128 and 128 √ 3

B
64 and -64 √ 3

C
512 and -512 √ 3

D
None of these
Question 20
1 / -0

The equation │4z - 1│ = 4 │z - 5│ represents

A
a straight line

B
a circle

C
a parabola

D
an ellipse