(1-6i)(-5+8i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (1 - 6i)(-5 + 8i)

This article will demonstrate how to multiply two complex numbers: (1 - 6i) and (-5 + 8i).

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, similar to multiplying binomials.

1. Expand the product: (1 - 6i)(-5 + 8i) = (1)(-5) + (1)(8i) + (-6i)(-5) + (-6i)(8i)

2. Simplify the terms: = -5 + 8i + 30i - 48i²

3. Substitute i² with -1: = -5 + 8i + 30i - 48(-1)

4. Combine real and imaginary terms: = (-5 + 48) + (8 + 30)i

5. Simplify the result: = 43 + 38i

Conclusion

Therefore, the product of (1 - 6i) and (-5 + 8i) is 43 + 38i.