The imaginary unit i satisfies i^2 = -1. Which option correctly states this?

The imaginary unit i satisfies i^2 = -1. Which option correctly states this?

• A. -1
• B. 0
• C. 1
• D. undefined

Answer: (A)

Imaginary unit i is defined by the property that its square is negative one. This definition enables solving equations like x^2 + 1 = 0, which has no real solution. Because of this, i^2 equals -1, which is exactly the statement asked for. The other values don’t fit: 0 would force i to be 0, and 1 would force i to be 1, contradicting the defining property. Undefined would suggest no such number exists, but in the complex numbers i is precisely the number that satisfies i^2 = -1. You can also see the pattern in the powers of i: i^2 = -1, i^3 = -i, i^4 = 1, and it repeats.

Imaginary unit i is defined by the property that its square is negative one. This definition enables solving equations like x^2 + 1 = 0, which has no real solution. Because of this, i^2 equals -1, which is exactly the statement asked for. The other values don’t fit: 0 would force i to be 0, and 1 would force i to be 1, contradicting the defining property. Undefined would suggest no such number exists, but in the complex numbers i is precisely the number that satisfies i^2 = -1. You can also see the pattern in the powers of i: i^2 = -1, i^3 = -i, i^4 = 1, and it repeats.