Question

State true or false for the following:

The argument of the complex number z = `(1 + i sqrt(3))(1 + i)(cos theta + i sin theta)` is `(7pi)/12 + theta`.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

arg(z) = arg`(1 + i sqrt(3))` + arg(1 + i) + arg(cosθ + isinθ)

`pi/3 + pi/4 + theta`

= `(7pi)/12 + theta`