(−4+2i)⋅(4−4i)

Jasonbradley

2 min read

·

Jun 17, 2024

14

Share

Multiplying Complex Numbers: (−4+2i)⋅(4−4i)

This article explores the process of multiplying two complex numbers: (−4+2i)⋅(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 follow the distributive property, similar to multiplying binomials:

1. Expand the product: (−4+2i)⋅(4−4i) = (−4)(4) + (−4)(-4i) + (2i)(4) + (2i)(-4i)

2. Simplify: = -16 + 16i + 8i - 8i²

3. Substitute i² with -1: = -16 + 16i + 8i + 8

4. Combine real and imaginary terms: = (-16 + 8) + (16 + 8)i

5. Final result: = -8 + 24i

Conclusion

Therefore, the product of (−4+2i) and (4−4i) is -8 + 24i. This process demonstrates how complex numbers can be multiplied using the distributive property and the fundamental property of the imaginary unit, i² = -1.