What is the square root of -1?

What is the square root of -1?

• A. 1
• B. i or j
• C. 0
• D. Undefined

Answer: (B)

The key idea is imaginary numbers: we extend the real numbers so that a number can square to a negative value. No real number satisfies x^2 = -1, so the square root of -1 doesn’t exist among real numbers. Introducing the imaginary unit i with i^2 = -1 gives a number whose square is -1, so the square root of -1 is i. In engineering contexts, the same concept uses j instead of i, so you can say the square root of -1 is i or j. Note there are two roots, ±i (or ±j), but i (or j) is the conventional representation for the principal square root.

The key idea is imaginary numbers: we extend the real numbers so that a number can square to a negative value. No real number satisfies x^2 = -1, so the square root of -1 doesn’t exist among real numbers. Introducing the imaginary unit i with i^2 = -1 gives a number whose square is -1, so the square root of -1 is i. In engineering contexts, the same concept uses j instead of i, so you can say the square root of -1 is i or j. Note there are two roots, ±i (or ±j), but i (or j) is the conventional representation for the principal square root.