Question

If z = x + 3i, then value of ${\int }_2^4\left[arg\left|\frac{z-i}{z+i}\right|\right]dx$ is ___. $|\cdot |$ represents modulus of a complex numbers

Answer 1

$\left|\frac{z-i}{z+i}\right|$=purely real number
$\therefore arg\left|\frac{z-i}{z+i}\right|=0{\int }_2^4\left[0\right]dx=0$