Complex Numbers Test

Result

Complex Numbers Test - 27

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Weekly Quiz Competition

Question 1
4 / -1

The value of the expression

A

B

C

D
None of these

Solution
Question 2
4 / -1

The value of

A
1

B
- 1

C
- i

D
i

Solution
Question 3
4 / -1

If z ≠ 1 and z²/(z - 1)is real, then the point represented by the complex number z lies

A
either on the real axis or on a circle passing through the origin

B
on a circle with centre at the origin

C
either on the real axis or on a circle not passing through the origin

D
on the imaginary axis

Solution
Question 4
4 / -1

The shaded region, where P = (-1, 0), Q = (-1 + √2, √2) R = (-1 + √2, -√2), S = (1,0) is represented by

A
|z + 1| > 2, arg (z + 1) < π/4

B
|z + 1| < 2, arg (z + 1) < π/4

C
|z - 1| > 2, arg (z + 1) > π/4

D
|z - 1| < 2, arg (z + 1) > π/4

Solution
Question 5
4 / -1

A
π/2

B
π/6

C
2π/3

D
5π/6
Question 6
4 / -1

A
10π/3

B
20π/3

C
16π/3

D
32π/3

Solution
Question 7
4 / -1

A
1

B
–1

C
i

D
–i

Solution
Question 8
4 / -1

A
0

B
1

C
2

D
3

Solution
Question 9
4 / -1

The cube roots of unity lie on the circle

A
| z | = 1

B
| z − 1 | = 1

C
| z + 1 | = 1

D
| z − ω| = 1

Solution
Question 10
4 / -1

If ω( ≠ 1) is a cube root of unity and (1 + ω)⁷ = A + Bω, then A and B are respectively

A
0, 1

B
1, 1

C
1, 0

D
−1, 1

Solution