Simplify the expression 5 5i 6 3i – Simplifying mathematical expressions is a fundamental skill in algebra that involves transforming complex expressions into simpler, equivalent forms. In this guide, we embark on a step-by-step journey to simplify the expression 5 + 5i + 6 + 3i, delving into the concepts of like terms, imaginary numbers, and the rules of algebraic operations.
As we progress, we will uncover the significance of simplified expressions and their applications in various mathematical contexts, empowering you with a deeper understanding of algebraic manipulations.
Simplifying the Expression 5 + 5i + 6 + 3i
Simplifying mathematical expressions involves combining like terms and performing arithmetic operations to obtain a more concise and manageable form of the expression. In this article, we will simplify the expression 5 + 5i + 6 + 3i, where i represents the imaginary unit.
Combining Like Terms
Like terms in algebra are terms that have the same variable raised to the same power. In our expression, the terms 5 and 6 are like terms because they both represent real numbers. Similarly, the terms 5i and 3i are like terms because they both represent imaginary numbers multiplied by i.
To combine like terms, we simply add their numerical coefficients. Therefore, 5 + 6 = 11 and 5i + 3i = 8i.
Simplifying the Imaginary Part
Imaginary numbers are numbers that are multiplied by the imaginary unit i. The imaginary unit is defined as i = √(-1). This means that i 2= -1. Using this property, we can simplify the imaginary part of our expression.
8i = 8 – √(-1) = √(64 – (-1)) = √(-64) = 8i
Writing the Simplified Expression, Simplify the expression 5 5i 6 3i
Combining the simplified real and imaginary parts, we get the final simplified expression:
5 + 5i + 6 + 3i = 11 + 8i
This simplified expression is more concise and easier to work with in further calculations.
Q&A: Simplify The Expression 5 5i 6 3i
What is the concept of simplifying mathematical expressions?
Simplifying mathematical expressions involves transforming complex expressions into simpler, equivalent forms by applying algebraic operations such as combining like terms and simplifying imaginary parts.
What are like terms in algebra?
Like terms are terms that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.
How do you simplify the imaginary part of an expression?
To simplify the imaginary part, apply the rules for adding and subtracting imaginary numbers, which involve combining coefficients of the imaginary unit i.
