Solving equation involving cube root of a complex number

Solving equation involving cube root of a complex number

IB Year 6 | Grade 12

If \((x+iy)^{\frac{1}{3}}=a+ib\), where \(x,y,a,b\in\mathbb R\) and \(ab\ne0\), show that \(4(a^2-b^2)=\frac{x}{a}+\frac{y}{b}\).

Solution:

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Answer:\(\frac xa+\frac yb=4(a^2-b^2)\), proved using \(a,b\ne0\).

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