(x+4i)(x-4i)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x + 4i)(x - 4i) = 0

This equation involves complex numbers, where 'i' represents the imaginary unit (√-1). Let's break down how to solve it:

Understanding Complex Numbers

A complex number has the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit.

• Real Part: The real part of the complex number is 'a'.
• Imaginary Part: The imaginary part of the complex number is 'b'.

Solving the Equation

1. Recognize the Pattern: The given equation (x + 4i)(x - 4i) = 0 is in the form of the difference of squares: (a + b)(a - b) = a² - b²

2. Apply the Difference of Squares: Applying this pattern, we get:

   x² - (4i)² = 0

3. Simplify: Remember that i² = -1. Therefore:

   x² - 16(-1) = 0 x² + 16 = 0

4. Solve for x: Subtract 16 from both sides:

   x² = -16 x = ±√(-16) x = ±4i

The Solutions

The solutions to the equation (x + 4i)(x - 4i) = 0 are x = 4i and x = -4i. These are both complex numbers.

Conclusion

This equation demonstrates how the difference of squares pattern can be applied even when dealing with complex numbers. The solutions illustrate that complex equations can have complex number solutions.