When we take the square root of something, we ask the question: which positive number can we square to get this number?

For example, we know that the square root of 25 is 5, because 5 is the only positive number which we can square to make 25. We can do the same for any positive number, including 0.

But what about negative numbers? Unfortunately, there is no positive number which we can square to get a negative number. We know this, because the square of any number is always positive (or 0, because 0 squared is 0).

Therefore, we must define a new object, called an imaginary unit, which we will call 'i'. We define i like this:

By doing this, we can now write down what the square root of -9 is. It is 3i, because:

-3i is also a square root of -9, but just as when we were taking the square roots of real numbers, we have a 'principal' square root which gives us only one of the square roots -- in this case, 3i, not -3i.

Your calculator can't deal with imaginary units, which is why it gives you an error message.

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