(4-i)(2+5i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (4 - i)(2 + 5i)

This article will walk through the process of multiplying the complex numbers (4 - i) and (2 + 5i).

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.

Multiplication Process

To multiply complex numbers, we use the distributive property, just like with regular binomials.

1. Expand the product: (4 - i)(2 + 5i) = 4(2 + 5i) - i(2 + 5i)

2. Distribute: = 8 + 20i - 2i - 5i²

3. Simplify by remembering i² = -1: = 8 + 20i - 2i + 5

4. Combine real and imaginary terms: = (8 + 5) + (20 - 2)i

5. Final answer: = 13 + 18i

Conclusion

Therefore, the product of (4 - i) and (2 + 5i) is 13 + 18i.