Simplifying Complex Numbers: (65i)+(2i)2(5+6i)
This article will walk you through the process of simplifying the complex expression (65i)+(2i)2(5+6i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where:
 a and b are real numbers
 i is the imaginary unit, defined as the square root of 1 (i.e., i² = 1)
Simplifying the Expression

Distribute: Begin by distributing the 2 to the terms inside the parentheses: (65i)+(2i)2(5+6i) = (65i)+(2i) + 10  12i

Combine Real and Imaginary Terms: Group the real terms and the imaginary terms together: (6 + 2 + 10) + (5  1  12)i

Simplify: Combine the like terms: 18  18i
The Solution
Therefore, the simplified form of (65i)+(2i)2(5+6i) is 18  18i.