%2B(9-4i%5E4).jpeg "(5+4i^2)+(9-4i^4)")
Simplifying Complex Numbers: (5 + 4i²) + (9 - 4i⁴)
This article will walk you through the process of simplifying the complex number expression (5 + 4i²) + (9 - 4i⁴).
Understanding the Basics
- 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, defined as the square root of -1 (i² = -1).
- Simplifying Complex Numbers: The goal is to express the complex number in the standard form a + bi. This involves simplifying any powers of i.
Simplifying the Expression
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Simplify i² and i⁴:
- We know i² = -1.
- i⁴ = (i²)² = (-1)² = 1.
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Substitute the values:
- (5 + 4i²) + (9 - 4i⁴) becomes (5 + 4(-1)) + (9 - 4(1)).
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Simplify the expression:
- (5 - 4) + (9 - 4) = 1 + 5 = 6
Final Answer
Therefore, the simplified form of the complex number expression (5 + 4i²) + (9 - 4i⁴) is 6.