%5E2.jpeg "(-5i)^2")
Simplifying (-5i)²
In mathematics, understanding how to simplify expressions involving imaginary numbers is crucial. Let's delve into the simplification of (-5i)².
Understanding Imaginary Numbers
Imaginary numbers, denoted by the symbol i, are defined as the square root of -1. This means:
i² = -1
This property is essential for simplifying expressions involving imaginary numbers.
Simplifying (-5i)²
To simplify (-5i)², we can apply the rules of exponents and the definition of i²:
- Expand the square: (-5i)² = (-5i) * (-5i)
- Multiply the terms: (-5i) * (-5i) = 25i²
- Substitute i² with -1: 25i² = 25 * (-1)
- Simplify: 25 * (-1) = -25
Therefore, (-5i)² simplifies to -25.
Key Takeaways
- The square of an imaginary number is always a real number.
- Simplifying expressions involving imaginary numbers often involves using the property i² = -1.
By understanding these concepts, you can confidently work with imaginary numbers and simplify expressions involving them.