Question

If z ≠ 0, then `int_(x = 0)^100` [arg | z |] dx is ______.

(where [.] denotes the greatest integer function)

Options

• 0

• 10

• 100

• Not defined

Answer 1

If z ≠ 0, then `int_(x = 0)^100` [arg | z |] dx is 0.

(where [.] denotes the greatest integer function)

Explanation:

∵ | z | = real and positive and imaginary part is zero.

∴ arg | z | = 0

`\implies` [arg | z |] = 0

∴ `int_(x = 0)^100` [arg | z |] dx = `int_(x = 0)^100` 0 dx = 0