(5+4i^2)+(9-4i^4)

Jasonbradley

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Jun 16, 2024

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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

1. Simplify i² and i⁴:

   • We know i² = -1.
   • i⁴ = (i²)² = (-1)² = 1.

2. Substitute the values:

   • (5 + 4i²) + (9 - 4i⁴) becomes (5 + 4(-1)) + (9 - 4(1)).

3. 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.