(2−2i)⋅(4−4i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (2-2i)⋅(4-4i)

This article will guide you through the process of multiplying the complex numbers (2-2i) and (4-4i).

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 (i² = -1).

Multiplication Process

To multiply complex numbers, we can use the distributive property (also known as FOIL method) just like with regular binomials:

(2-2i)⋅(4-4i) = 2(4-4i) - 2i(4-4i)

Expanding the terms:

= 8 - 8i - 8i + 8i²

Since i² = -1, we can substitute:

= 8 - 8i - 8i - 8

Combining the real and imaginary terms:

= -16i

Conclusion

Therefore, the product of (2-2i) and (4-4i) is -16i, a purely imaginary number.