(3-2i)(4+i)

Jasonbradley

2 min read

·

Jun 16, 2024

11

Share

Multiplying Complex Numbers: (3-2i)(4+i)

This article will guide you through the process of multiplying two complex numbers: (3 - 2i) and (4 + i).

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).

Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property, similar to how we multiply binomials.

1. Expand the product: (3 - 2i)(4 + i) = 3(4 + i) - 2i(4 + i)

2. Apply the distributive property: = (3 * 4) + (3 * i) + (-2i * 4) + (-2i * i)

3. Simplify the terms: = 12 + 3i - 8i - 2i²

4. Substitute i² with -1: = 12 + 3i - 8i - 2(-1)

5. Combine like terms: = 12 + 2 + 3i - 8i

6. Simplify the result: = 14 - 5i

Conclusion

Therefore, the product of (3 - 2i) and (4 + i) is 14 - 5i.