(1-9i)(1-4i)(4-3i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (1-9i)(1-4i)(4-3i)

This article will guide you through the process of multiplying the complex numbers (1-9i)(1-4i)(4-3i).

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 we do with real numbers. Remember that i² = -1.

Step-by-Step Solution

1. Multiply the first two complex numbers:

   (1-9i)(1-4i) = 1 - 4i - 9i + 36i² = 1 - 13i - 36 = -35 - 13i

2. Multiply the result from step 1 with the third complex number:

   (-35 - 13i)(4-3i) = -140 + 105i - 52i + 39i² = -140 + 53i - 39 = -179 + 53i

Conclusion

Therefore, the product of the complex numbers (1-9i)(1-4i)(4-3i) is -179 + 53i.