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 \(i^2=-1\).
by
Arron Kau