Simplifying (−11−10i)<sup>2</sup>
In mathematics, simplifying complex numbers often involves understanding the concept of complex number multiplication and the imaginary unit (i). Let's break down how to simplify the expression (−11−10i)<sup>2</sup>.
Understanding Complex Number Multiplication
When multiplying complex numbers, we essentially use the distributive property similar to multiplying binomials. Remember that i<sup>2</sup> = 1.
Simplifying the Expression

Expand the square: (−11−10i)<sup>2</sup> = (−11−10i) * (−11−10i)

Apply the distributive property: = (11 * 11) + (11 * 10i) + (10i * 11) + (10i * 10i)

Simplify each term: = 121 + 110i + 110i + 100i<sup>2</sup>

Substitute i<sup>2</sup> with 1: = 121 + 110i + 110i + 100(1)

Combine like terms: = 121  100 + 110i + 110i

Final Result: = 21 + 220i
Therefore, the simplified form of (−11−10i)<sup>2</sup> is 21 + 220i.