Obtaining the roots of a complex number
Obtaining the roots of a complex number
IB Year 6 | Grade 12
Find all the complex numbers \(z\) such that
- \(z^4 = -16\)
- \(z^3 = -27i\)
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Answer:(a) \(z=\sqrt2-\sqrt2 i,\ \sqrt2+\sqrt2 i,\ -\sqrt2+\sqrt2 i,\ -\sqrt2-\sqrt2 i\) (b) \(z=\dfrac{3\sqrt3}{2}-\dfrac32i,\ 3i,\ -\dfrac{3\sqrt3}{2}-\dfrac32i\)
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