Question

How do you get from (-1)^(1/3) to 1/2+(i sqrt(3))/2?

Answer 1

The Function is (-1)^(1/3)

Re-write the function as

(1(-1+0i))^(1/3)

= (1)^(1/3) * (-1 + 0i)^(1/3)

= 1 * (-1 + 0i)^(1/3)

= (-1 + 0i)^(1/3)

= ( cos(π) +  isin(π) )^(1/3)

We know that De-moivre's Theorem

Therefore we can write

Therefore .