(x-2i)(x+2i)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x - 2i)(x + 2i) = 0

This equation involves complex numbers and presents a simple example of how to solve equations with complex factors. Let's break down the process step-by-step:

Understanding 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).

Solving the Equation

1. Zero Product Property: The equation (x - 2i)(x + 2i) = 0 relies on the zero product property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

2. Setting Factors to Zero: Therefore, to solve the equation, we set each factor equal to zero:

   • x - 2i = 0
   • x + 2i = 0

3. Solving for x: Solving each equation for 'x' gives us:

   • x = 2i
   • x = -2i

The Solutions

The solutions to the equation (x - 2i)(x + 2i) = 0 are x = 2i and x = -2i. These solutions are complex numbers, reflecting the nature of the factors in the original equation.

Significance

This simple example demonstrates how complex numbers can be used in algebraic equations. Understanding how to work with complex numbers is essential in various fields like electrical engineering, physics, and mathematics.