%5E4.jpeg "(5i)^4")
Understanding (5i)^4
This article explores the simplification of the expression (5i)^4 , where i represents the imaginary unit.
Imaginary Unit (i)
The imaginary unit i is defined as the square root of -1:
- i = √-1
This implies that i² = -1. This property is crucial for simplifying expressions involving i.
Simplifying (5i)^4
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Expand the expression: (5i)^4 = (5i) * (5i) * (5i) * (5i)
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Apply the properties of exponents: (5i)^4 = 5^4 * i^4
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Simplify the powers: 5^4 = 625 and i^4 = (i²)² = (-1)² = 1
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Substitute the simplified values: (5i)^4 = 625 * 1 = 625
Final Result
Therefore, (5i)^4 = 625. This demonstrates how the properties of imaginary numbers and exponents can be used to simplify complex expressions.