Question

The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______

Options

• `pi/3`

• `pi/4`

• `pi/5`

• `pi/6`

Answer 1

The argument of the complex number `(4 + 9i)/(13 + 5i)` is `underline(pi/4)`.

Explanation:

arg`((4 + 9i)/(13 + 5i)) = "arg"(4 + 9i) - "arg"(13 + 5i)`

= `tan^-1(9/4) - tan^-1(5/13)`

= `tan^-1 1`

= `pi/4`