(2-3i).jpeg "(6-2i)(2-3i)")
Multiplying Complex Numbers: (6-2i)(2-3i)
This article will walk through the process of multiplying the complex numbers (6-2i) and (2-3i).
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.
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property (also known as FOIL - First, Outer, Inner, Last).
1. Expand the product: (6-2i)(2-3i) = 6(2-3i) - 2i(2-3i)
2. Distribute: = 12 - 18i - 4i + 6i²
3. Simplify using i² = -1: = 12 - 18i - 4i - 6
4. Combine real and imaginary terms: = (12-6) + (-18-4)i
5. Final result: = 6 - 22i
Conclusion
Therefore, the product of (6-2i) and (2-3i) is 6 - 22i.