Now here's why De Moivre's theorem is so useful: it still holds, even if the power is a fraction. So we can find square roots, cube roots or any other roots, of complex numbers!
For example, consider the complex number z=4(cos60o+isin60o). Then we can write down the square root of z very quickly, we just raise the modulus to the power of one half and multiply the angle by one half:
If we have a complex number in its Cartesian form, we can find its square root or cube root, etc., by first converting it into its polar form, then using De Moivre's theorem. Here's an example of that:
Find the cube root of z if
You have a go first then check your answer.