(−2+2i)⋅(5+5i)

Jasonbradley

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Jun 17, 2024

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Multiplying Complex Numbers: (−2+2i)⋅(5+5i)

This article will guide you through the process of multiplying two complex numbers, specifically: (−2+2i)⋅(5+5i).

Understanding Complex Numbers

Before we delve into the multiplication, let's refresh our understanding of complex numbers:

• Complex numbers are numbers of 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 follow a similar approach to multiplying binomials:

1. Expand using the distributive property (FOIL method):

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

2. Simplify the terms:

   = -10 - 10i + 10i + 10i²

3. Substitute i² with -1:

   = -10 - 10i + 10i - 10

4. Combine real and imaginary terms:

   = (-10 - 10) + (-10 + 10)i

5. Final result:

   = -20

Conclusion

Therefore, the product of (−2+2i)⋅(5+5i) is -20. It's important to note that the result is a real number, even though we started with two complex numbers.