Polar Form of a Complex Number

Algebra Level 3

The complex number x=3−ix= \sqrt{3} - i can be expressed in polar form x=r(cos⁡θ+isin⁡θ)x = r\left(\cos\theta + i\sin\theta \right), where rr is a positive real number and 0≤θ≤2π0 \leq \theta \leq 2\pi. In fact, θ=aπb\theta = \frac{a\pi}{b} where aa and bb are coprime positive integers. What is the value of a+ba+b?

Details and assumptions

ii is the imaginary unit, where i2=−1i^2=-1.

Arron Kau by Arron Kau
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