(2-5i)(2+5i)

Jasonbradley

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Jun 16, 2024

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

This article will explore the process of multiplying the complex numbers (2 - 5i) and (2 + 5i). We'll use the distributive property and the fact that i² = -1 to simplify the expression.

Steps

1. Distribute:

   • (2 - 5i)(2 + 5i) = 2(2 + 5i) - 5i(2 + 5i)

2. Expand:

   • = 4 + 10i - 10i - 25i²

3. Simplify:

   • = 4 + 10i - 10i - 25(-1)
   • = 4 + 10i - 10i + 25

4. Combine like terms:

   • = 4 + 25 = 29

Conclusion

The product of (2 - 5i) and (2 + 5i) is 29. This result demonstrates a key concept: the product of a complex number and its complex conjugate always results in a real number.

Note: The complex conjugate of a complex number of the form a + bi is a - bi. In this case, (2 - 5i) is the conjugate of (2 + 5i).