(2+5i)(-1+5i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (2 + 5i)(-1 + 5i)

This article will guide you through the process of multiplying two complex numbers: (2 + 5i) and (-1 + 5i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where:

• a and b are real numbers.
• i is the imaginary unit, defined as the square root of -1 (i² = -1).

Multiplying Complex Numbers

To multiply two complex numbers, we use the distributive property, just like we do with real numbers. This means we multiply each term in the first complex number by each term in the second complex number.

Let's break down the multiplication of (2 + 5i)(-1 + 5i):

1. Distribute: (2 + 5i)(-1 + 5i) = 2(-1 + 5i) + 5i(-1 + 5i)

2. Expand: = -2 + 10i - 5i + 25i²

3. Simplify: = -2 + 5i + 25(-1) (Remember i² = -1) = -2 + 5i - 25

4. Combine real and imaginary terms: = -27 + 5i

Conclusion

Therefore, the product of (2 + 5i) and (-1 + 5i) is -27 + 5i.