#1**0 **

Rewrite as follows:

\({x^2}^2 = -4\)

Take the square root of both sides:

\(x^2 = 2i\)

Take the square root again:

\(\color{brown}\boxed{x = 1 + i}\)

BuilderBoi Apr 13, 2022

#3**0 **

The remaining 3 are very similar to \(1 + i\). You can find them yourself by taking the inverse(s) of 1 or both terms.

BuilderBoi
Apr 13, 2022

#4**0 **

After you find the first root 1 + i

you can picture finding the other roots by making (around the origin)

a 90^{o} rotation, giving you -1 + i

a 180^{o} rotation, giving you -1 - i

a 270^{o} rotation, giving you 1 - i

A 360^{o} rotation will take you back to your original root.

There will be four fourth roots, separated by 90^{o} [ 360^{o} / 4 = 90^{o} ]

There will be three third roots, separated by 120^{o}

There will be five fifth roots, separated by 72^{o}

Etc.

geno3141 Apr 13, 2022