Multiplying Complex Numbers: (5  6i)(6  2i)
This article will demonstrate how to multiply two complex numbers, (5  6i) and (6  2i).
Understanding Complex Numbers
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 (i² = 1).
Multiplication Process
To multiply complex numbers, we use the distributive property, just like with any binomial multiplication.

Expand the product: (5  6i)(6  2i) = 5(6  2i)  6i(6  2i)

Apply the distributive property: = 30  10i  36i + 12i²

Substitute i² with 1: = 30  10i  36i + 12(1)

Combine real and imaginary terms: = (30  12) + (10  36)i

Simplify: = 18  46i
Result
Therefore, the product of (5  6i) and (6  2i) is 18  46i.
This process is straightforward and can be applied to any multiplication of complex numbers. Remember to distribute carefully, substitute i² with 1, and combine like terms to reach the final simplified form.