(7+2i)(-6+8i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (7 + 2i)(-6 + 8i)

This article will guide you through the process of multiplying two complex numbers: (7 + 2i)(-6 + 8i).

Understanding Complex Numbers

Complex numbers are numbers that consist of a real part and an imaginary part. They are typically written 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 (i.e., i² = -1).

Multiplication Process

To multiply complex numbers, we follow the distributive property, just like multiplying binomials.

1. Expand the product: (7 + 2i)(-6 + 8i) = 7(-6 + 8i) + 2i(-6 + 8i)

2. Distribute: = -42 + 56i - 12i + 16i²

3. Simplify using i² = -1: = -42 + 56i - 12i - 16

4. Combine real and imaginary terms: = (-42 - 16) + (56 - 12)i

5. Final result: = -58 + 44i

Therefore, the product of (7 + 2i)(-6 + 8i) is -58 + 44i.