+2666 Rewrite as follows:
\({x^2}^2 = -4\)
Take the square root of both sides:
\(x^2 = 2i\)
Take the square root again:
\(\color{brown}\boxed{x = 1 + i}\)
+2666 The remaining 3 are very similar to \(1 + i\). You can find them yourself by taking the inverse(s) of 1 or both terms.
+23245 After you find the first root 1 + i
you can picture finding the other roots by making (around the origin)
a 90o rotation, giving you -1 + i
a 180o rotation, giving you -1 - i
a 270o rotation, giving you 1 - i
A 360o rotation will take you back to your original root.
There will be four fourth roots, separated by 90o [ 360o / 4 = 90o ]
There will be three third roots, separated by 120o
There will be five fifth roots, separated by 72o
Etc.
