Multiplying Complex Numbers: (7i3)(2+6i)
This article will guide you through the process of multiplying two complex numbers: (7i3)(2+6i).
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.
Multiplication Process
We can multiply complex numbers using the distributive property, similar to multiplying binomials:

Distribute the first term of the first complex number: (7i  3) * 2 = 14i  6

Distribute the second term of the first complex number: (7i  3) * 6i = 42i²  18i

Combine the results: 14i  6 + 42i²  18i

Simplify using the fact that i² = 1: 14i  6  42  18i

Combine like terms: 48  4i
The Result
Therefore, the product of (7i3)(2+6i) is 48  4i.
Conclusion
Multiplying complex numbers involves applying the distributive property and simplifying using the fact that i² = 1. This process leads to a new complex number, in this case, 48  4i.