(6-2i)(2-3i) In Standard Form

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (6-2i)(2-3i) in Standard Form

This article will guide you through the process of multiplying the complex numbers (6-2i) and (2-3i) and expressing the result in standard form (a + bi).

Understanding Complex Numbers

Complex numbers are expressed in the form a + bi, where:

• a is the real part
• b is the imaginary part
• i is the imaginary unit, defined as the square root of -1 (i² = -1)

Multiplication of Complex Numbers

When multiplying complex numbers, we treat them like binomials and use the distributive property (or FOIL method):

(6 - 2i)(2 - 3i) = (6 * 2) + (6 * -3i) + (-2i * 2) + (-2i * -3i)

Simplifying the Expression

1. Multiply the terms: 12 - 18i - 4i + 6i²

2. Substitute i² with -1: 12 - 18i - 4i + 6(-1)

3. Combine real and imaginary terms: (12 - 6) + (-18 - 4)i

4. Simplify: 6 - 22i

Final Result

Therefore, the product of (6-2i) and (2-3i) in standard form is 6 - 22i.