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Area of the triangle formed by cube roots

Area of the triangle formed by cube roots

IB Year 6 | Grade 12
  1. Find the cube roots of \(8i\), giving your answers in polar form.
  2. If the cube roots of \(8i\) are represented by points \(A\), \(B\) and \(C\) on an Argand diagram, find the area of triangle \(ABC\).

Solution:

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Answer:(a) \(2\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right),\ 2\left(\cos\frac{5\pi}{6}+i\sin\frac{5\pi}{6}\right),\ 2\left(\cos\left(-\frac{\pi}{2}\right)+i\sin\left(-\frac{\pi}{2}\right)\right)\) (b) \(3\sqrt3\)

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