Polar Form of a Complex Number

Algebra Level 2

The complex number \(x= \sqrt{3} - i\) can be expressed in polar form \(x = r\left(\cos\theta + i\sin\theta \right)\), where \(r\) is a positive real number and \(0 \leq \theta \leq 2\pi\). In fact, \(\theta = \frac{a\pi}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

Details and assumptions

\(i \) is the imaginary unit, where \(i^2=-1\).

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