(9+4i)(2-3i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (9 + 4i)(2 - 3i)

This article will guide you through the process of multiplying two complex numbers: (9 + 4i) and (2 - 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 (i² = -1).

Multiplication Process

To multiply complex numbers, we use the distributive property, similar to multiplying binomials:

1. Expand the product:

   (9 + 4i)(2 - 3i) = 9(2 - 3i) + 4i(2 - 3i)

2. Distribute:

   = 18 - 27i + 8i - 12i²

3. Substitute i² with -1:

   = 18 - 27i + 8i + 12

4. Combine real and imaginary terms:

   = (18 + 12) + (-27 + 8)i

5. Simplify:

   = 30 - 19i

Conclusion

Therefore, the product of (9 + 4i) and (2 - 3i) is 30 - 19i. This demonstrates how to multiply complex numbers using the distributive property and the definition of the imaginary unit.