Mathematics - Complex Number

Test Preparation on Mathematics - Complex Number

1.

If the cube roots of unity are 1, w,w²then the roots of the equation

(x−1)³+8=0 are-

1
- 1, - 1 + 2w, - 1 - 2w²
2
- 1, - 1, - 1,
3
- 1, 1 - 2w, 1 - 2w²
4
- 1, 1 + 2w, 1 + 2w²

2.

If z1 and z2 are two non-zero complex numbers such that l z1 + z2 l = l z1 l + l z2 l, then arg z1 - arg z2 is equal to

12π
2- π
30
4-π/2

3.

If w =z/z-1/3i and l w l = 1, then z lies on

1an ellipse
2a circle
3a straig t line
4a parabola

4.

Let z, w be complex numbers such that z + i w = 0 and arg zw = π. Then arg z equals-

1π/4
2π/2
33π/4
45π/4

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