(-4+6i)(2-i)(3+7i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of multiplying the complex numbers (-4+6i)(2-i)(3+7i).

Understanding Complex Numbers

Complex numbers are numbers 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.

Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property, just like multiplying binomials. Remember that i² = -1.

Step-by-Step Solution

1. Multiply the first two complex numbers: (-4 + 6i)(2 - i) = (-4 * 2) + (-4 * -i) + (6i * 2) + (6i * -i) = -8 + 4i + 12i - 6i² = -8 + 16i + 6 (since i² = -1) = -2 + 16i

2. Multiply the result from step 1 by the third complex number: (-2 + 16i)(3 + 7i) = (-2 * 3) + (-2 * 7i) + (16i * 3) + (16i * 7i) = -6 - 14i + 48i + 112i² = -6 + 34i - 112 (since i² = -1) = -118 + 34i

Conclusion

Therefore, the product of the complex numbers (-4 + 6i)(2 - i)(3 + 7i) is -118 + 34i.