# How do you solve # sqrtz=-1#?

##### 2 Answers

#### Explanation:

Square both sides,

There is no solution.

#### Explanation:

By definition, for **real numbers**,

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,

(1)

#(bi)^2 = -n# , and

(2)#b > 0#

For complex numbers more generally, there is no consensus on a "principle" square root.

So there is no principle square root of