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:

Expand using the distributive property (FOIL method):
(2 + 2i)(5 + 5i) = (2 * 5) + (2 * 5i) + (2i * 5) + (2i * 5i)

Simplify the terms:
= 10  10i + 10i + 10i²

Substitute i² with 1:
= 10  10i + 10i  10

Combine real and imaginary terms:
= (10  10) + (10 + 10)i

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.