Problem 45 - Introductory Algebra for College Students

Question

What is the imaginary unit \(i ?\)

Step-by-Step Solution

Answer

The imaginary unit \(i\) is defined as the square root of -1, i.e., \( i = \sqrt{-1}\)

Step 1: Imaginary Unit Definition

In mathematics, the imaginary unit allows the real number system \(\mathbb{R}\) to be extended to the complex number system \(\mathbb{C}\), which includes the arithmetic of complex numbers. The imaginary unit is denoted by the symbol \(i\) and by the definition, it is a mathematical term used to describe the square root of -1. In other words, \( i = \sqrt{-1}\)

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Step 6: Conclude with the answer

The imaginary unit \(i\) is defined as the square root of -1, i.e., \( i = \sqrt{-1}\)