i^2=−1
(1 point)
Responses
True
True
False
True
True
The correct answer is "True." To understand why, let's break down the equation i^2 = -1 step by step:
1. First, let's define i. In mathematics, the imaginary unit is denoted by "i," which represents the square root of -1.
2. Now, let's square i. When you square a number, you multiply it by itself. So, i^2 means taking i and multiplying it by itself: i * i.
3. By applying the definition of i as the square root of -1, we have (sqrt(-1)) * (sqrt(-1)).
4. Multiplying the square roots: (sqrt(-1)) * (sqrt(-1)) = sqrt(-1 * -1) = sqrt(1) = 1.
5. Simplifying further, you get 1 as the result of squaring i.
6. However, the given equation i^2 = -1 states that the result is -1, not 1. Therefore, the statement i^2 = -1 is true.
Hence, the correct response is "True."