(7-2i)(7+2i)

2 min read Jun 16, 2024

Multiplying Complex Numbers: (7-2i)(7+2i)

This article will demonstrate the multiplication of the complex numbers (7-2i) and (7+2i).

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).

Multiplication Process

To multiply complex numbers, we use the distributive property (also known as FOIL - First, Outer, Inner, Last) just like we do with binomials.

Let's multiply (7-2i)(7+2i):

First: 7 * 7 = 49
Outer: 7 * 2i = 14i
Inner: -2i * 7 = -14i
Last: -2i * 2i = -4i²

Now, combining all the terms:

49 + 14i - 14i - 4i²

Since i² = -1, we can substitute:

49 + 14i - 14i - 4(-1)

Simplifying the expression:

49 + 4 = 53

Result

Therefore, the product of (7-2i) and (7+2i) is 53.

Important Note

Notice that the result is a real number. This is because (7-2i) and (7+2i) are complex conjugates of each other. The product of two complex conjugates always results in a real number.