Imaginary unit
The square root of the imaginary unit i is
Explanation
We square both sides of the equation and get
This means that the equation x2 − i = 0 has two solutions
and that is in accordance with the fundamental theorem of algebra, which states that any algebraic equation has a root within the system of complex numbers.
Note
The equation x2 + i = 0 has also two solutions
This means that
You can calculate it as
or by squaring both sides of this equation, so that
This shows that i, the square root of −1 is necessary and sufficient.