Multiplying Complex Numbers: (7 − 3i) ⋅ (2 − i)
This article will walk through the process of multiplying two complex numbers: (7 − 3i) ⋅ (2 − i).
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).
Multiplying Complex Numbers
Multiplying complex numbers is similar to multiplying binomials. We use the distributive property (or FOIL method) to expand the product.
Here's how to multiply (7 − 3i) ⋅ (2 − i):

Distribute: (7 − 3i) ⋅ (2 − i) = 7(2 − i) − 3i(2 − i)

Simplify: = 14 − 7i − 6i + 3i²

Substitute i² = 1: = 14 − 7i − 6i + 3(1)

Combine real and imaginary terms: = (14  3) + (7  6)i

Final result: = 11  13i
Therefore, the product of (7 − 3i) ⋅ (2 − i) is 11  13i.
Conclusion
Multiplying complex numbers involves using the distributive property and substituting i² with 1. This results in a new complex number with both a real and imaginary component.