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(6-5i)+(2-i)-2(-5+6i)

less than a minute read Jun 16, 2024
(6-5i)+(2-i)-2(-5+6i)

Simplifying Complex Numbers: (6-5i)+(2-i)-2(-5+6i)

This article will walk you through the process of simplifying the complex expression (6-5i)+(2-i)-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

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

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

  3. Simplify: Combine the like terms: 18 - 18i

The Solution

Therefore, the simplified form of (6-5i)+(2-i)-2(-5+6i) is 18 - 18i.

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