Direct nth roots: shifted or transformed variable

Questions that ask to solve (z + a)^n = w or similar equations where the variable is shifted or transformed, requiring an additional step to recover z after finding the nth roots.

1 questions · Standard +0.8

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CAIE Further Paper 2 2023 November Q2

5 marks Standard +0.8

2 Find the roots of the equation \(( z + 5 i ) ^ { 3 } = 4 + 4 \sqrt { 3 } i\), giving your answers in the form \(r \cos \theta + i ( r \sin \theta - 5 )\), where \(r > 0\) and \(0 < \theta < 2 \pi\).