(5-6i)(6-2i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (5 - 6i)(6 - 2i)

This article will demonstrate how to multiply two complex numbers, (5 - 6i) and (6 - 2i).

Understanding Complex Numbers

A complex number is a number 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, just like with any binomial multiplication.

1. Expand the product: (5 - 6i)(6 - 2i) = 5(6 - 2i) - 6i(6 - 2i)

2. Apply the distributive property: = 30 - 10i - 36i + 12i²

3. Substitute i² with -1: = 30 - 10i - 36i + 12(-1)

4. Combine real and imaginary terms: = (30 - 12) + (-10 - 36)i

5. Simplify: = 18 - 46i

Result

Therefore, the product of (5 - 6i) and (6 - 2i) is 18 - 46i.

This process is straightforward and can be applied to any multiplication of complex numbers. Remember to distribute carefully, substitute i² with -1, and combine like terms to reach the final simplified form.