Question

Polar form of the complex number \(z = -4 + i4\sqrt{3}\) is :

• A. \(8(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3})\)
• B. \(8(\cos\frac{\pi}{6} + i\sin\frac{\pi}{6})\)
• C. \(8(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3})\)
• D. \(8(\cos\frac{5\pi}{6} + i\sin\frac{5\pi}{6})\)

Hint:

To save time, check the signs of \(x\) and \(y\) first:
\(x = -4\) (negative) and \(y = 4\sqrt{3}\) (positive) puts the point in the second quadrant.
The only second-quadrant angle among the choices is \(\frac{2\pi}{3}\) (since \(\frac{\pi}{3}\) and \(\frac{\pi}{6}\) are in Quadrant I, and \(\frac{5\pi}{6}\) would require different coordinates).
This immediately points to Option (C).

Answer 1

The Correct Option is C