%5E2.jpeg "(-8i)^2")
Understanding (-8i)^2
In mathematics, especially when dealing with complex numbers, understanding how to square an imaginary number is crucial. Let's break down the process of calculating (-8i)^2.
Key Concepts
- Imaginary Unit (i): The imaginary unit, denoted by 'i', is defined as the square root of -1 (i.e., i^2 = -1).
- Complex Numbers: Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit.
Calculation Steps
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Squaring the Expression: (-8i)^2 means multiplying (-8i) by itself: (-8i) * (-8i)
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Applying Multiplication Rules: Remember that when multiplying two negative numbers, the result is positive. Also, we know that i^2 = -1. Therefore: (-8i) * (-8i) = 64i^2
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Substituting i^2: Replace i^2 with -1: 64 * (-1)
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Simplifying: -64
Result
Therefore, (-8i)^2 equals -64. This is a real number, despite starting with an imaginary number.