Yes it is an imaginary number
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The square roots of -81 are ±9i where i is the imaginary square root of -1.
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No - a square root of a negative number is an imaginary number. for example, sqrt(-9) is equal to 3i.
The usual rules for "order of operation" apply. Don't forget that the square root of a negative number is an imaginary number. As an example, the square root of -9 is 3i (that is, the square root of +9, times the "imaginary unit").
i is the symbol for an imaginary number, a complex number with the property i2=-1. The square root of a negative number is the square root times i. For example, the square root of -9 = 3i.