First, you can read about the definition of \(i\), Imaginary Unit in the Brilliant.org Algebra Glossary
Let
\(\sqrt[3]{\strut i}=\displaystyle \frac{\sqrt{a}+i}{b}\)
where \(a\) and \(b\) is positive integers and \(a\) is not a square number.
What is the value of \(a+b\)?
This problem is inspired by The Square Root of \(i\)?
by
Kai Hsien Boo
