(x-5i)(x+5i)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x - 5i)(x + 5i) = 0

This equation represents a simple quadratic equation with complex coefficients. Let's break down how to solve it:

Understanding Complex Numbers

Before we dive into the solution, let's remember that 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 - 5i)(x + 5i) = 0 utilizes the Zero Product Property, which 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 - 5i = 0
   • x + 5i = 0

3. Solving for x: Solving for 'x' in each equation, we get:

   • x = 5i
   • x = -5i

Solution

Therefore, the solutions to the equation (x - 5i)(x + 5i) = 0 are x = 5i and x = -5i.

Note

The solutions are complex conjugates of each other. This is a common pattern when dealing with quadratic equations involving complex numbers.