%5E4.jpeg "(-i)^4")
Understanding (-i)^4
In mathematics, the imaginary unit, denoted by i, is defined as the square root of -1. This means that i² = -1. Let's explore how to calculate (-i)⁴.
The Power of Exponents
When dealing with exponents, we understand that xⁿ means multiplying x by itself n times.
In our case, we need to calculate (-i) multiplied by itself four times.
Step by Step Calculation
-
(-i)²: Using the definition of i² = -1, we can rewrite this as (-1)² = 1.
-
(-i)⁴: Since (-i)² = 1, we can express (-i)⁴ as ( (-i)²)² = 1².
-
1²: This simplifies to 1.
Conclusion
Therefore, (-i)⁴ = 1.
This demonstrates that raising an imaginary unit to an even power results in a real number.