Multiplying Complex Numbers: (6 + 2i)(3i)
This article explores the multiplication of complex numbers, specifically the expression (6 + 2i)(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 (i² = 1).
Multiplication Process
To multiply complex numbers, we use the distributive property, just like we would with any binomial multiplication.

Distribute: (6 + 2i)(3i) = 6(3i) + 2i(3i)

Simplify: = 18i + 6i²

Substitute i² = 1: = 18i + 6(1)

Combine Real and Imaginary Terms: = 6 + 18i
Result
Therefore, the product of (6 + 2i) and (3i) is 6 + 18i.
Key Points
 Complex number multiplication involves multiplying both the real and imaginary components of the numbers.
 The distributive property is essential in simplifying these multiplications.
 Remember that i² = 1.
This example demonstrates a straightforward approach to multiplying complex numbers. It's a fundamental operation in various mathematical applications, particularly in areas like electrical engineering and quantum mechanics.