How do you solve # sqrtz=-1#?
Square both sides,
There is no solution.
By definition, for
It is true that every positive number has two square roots.
That means that for every positive number
The square root symbol (the square root function) denotes the non-negative solution.
Although it is true that
There is no solution to
If we are working in the complex numbers , the square root function is unchanged for positive real numbers.
For negative real number,
#(bi)^2 = -n#, and
#b > 0#
For complex numbers more generally, there is no consensus on a "principle" square root.
So there is no principle square root of