What is -i squared

General
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what is -i squared

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What is -i squared?

Answer: To understand what -i squared means, we need to start with the definition of the imaginary unit, denoted as i. By definition, i is the solution to the equation:

i^2 = -1

Given this information, we can proceed to find (-i)^2.

  1. Squaring -i:

Recall the properties of exponents for squaring a negative number and the imaginary unit:

(-i)^2 = (-i) \times (-i)
  1. Simplify the expression:

Using the fact that multiplying two negative quantities yields a positive quantity:

(-i) \times (-i) = (-1) \times i \times (-1) \times i

This can be rewritten using the associative property:

= (-1 \times -1) \times (i \times i)

We know that -1 \times -1 = 1, and from the definition of i:

(i \times i) = i^2 = -1

Therefore,

1 \times (-1) = -1

So,

(-i)^2 = -1

Conclusion: The value of (-i)^2 is \boxed{-1}.