# 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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