How to find the roots through the imaginary unit?

Question

Algebra

There was a task, to find the roots of the number -64 under the root with a base of 4, I still didn’t understand, the number is negative, and the base is even, how does it work? Explain, please

Answer 1

What is the fourth root of -64?
(-64)^(1/4) = (64*e ^{π*i + 2*π*i*n} )^(1/4) = 4*e ^{π/4*i + π/2*i*n}
Only 4 roots:
4*e ^±π/4 and 4*e ^±3π/4 , or by the Euler formula: ±2√2±2√2i