(−11−10i) 2

Jasonbradley

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Jun 17, 2024

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Simplifying (−11−10i)²

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)².

Understanding Complex Number Multiplication

When multiplying complex numbers, we essentially use the distributive property similar to multiplying binomials. Remember that i² = -1.

Simplifying the Expression

1. Expand the square: (−11−10i)² = (−11−10i) * (−11−10i)

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

3. Simplify each term: = 121 + 110i + 110i + 100i²

4. Substitute i² with -1: = 121 + 110i + 110i + 100(-1)

5. Combine like terms: = 121 - 100 + 110i + 110i

6. Final Result: = 21 + 220i

Therefore, the simplified form of (−11−10i)² is 21 + 220i.