Question

If $z\ne 0$ then ${\int }_0^{100}\left[arg|z|\right]dx$ is (where [.] denotes the greatest integer function)

• A. \N
• B. 10
• C. 100
• D. not defined

Answer 1

The correct option is A \N

$\because |z|=$ real and positive, imaginary part is zero
$\therefore arg|z|=0$
$\Rightarrow \left[arg|z|\right]=0$
$\therefore {\int }_0^{100}\left[arg|z|\right]dx={\int }_0^{100}0.dx=0$