Multiplying Complex Numbers: (92i)(3+i)
This article will guide you through the process of multiplying two complex numbers: (92i)(3+i).
Understanding Complex Numbers
Before we begin, let's quickly recap what complex numbers are. A complex number is a number 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.
The Multiplication Process
To multiply complex numbers, we use the distributive property (also known as FOIL  First, Outer, Inner, Last). This means we multiply each term in the first complex number by each term in the second complex number:

(92i)(3+i) = (9 * 3) + (9 * i) + (2i * 3) + (2i * i)

Simplify the terms: 27 + 9i  6i  2i²

Remember that i² = 1: 27 + 9i  6i + 2

Combine real and imaginary terms: (27 + 2) + (9  6)i

Final result: 29 + 3i
Conclusion
Therefore, the product of (92i) and (3+i) is 29 + 3i.
This example demonstrates how complex number multiplication is performed. The key is to remember the properties of the imaginary unit i, and use the distributive property to expand the product.