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(-11-7i)(2+6i)

2 min read Jun 16, 2024
(-11-7i)(2+6i)

Multiplying Complex Numbers: (-11 - 7i)(2 + 6i)

This article will guide you through the process of multiplying two complex numbers: (-11 - 7i) and (2 + 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)

Multiplication Process

To multiply complex numbers, we use the distributive property, similar to multiplying binomials.

  1. Expand the product: (-11 - 7i)(2 + 6i) = (-11 * 2) + (-11 * 6i) + (-7i * 2) + (-7i * 6i)

  2. Simplify each term: = -22 - 66i - 14i - 42i²

  3. Substitute i² with -1: = -22 - 66i - 14i - 42(-1)

  4. Combine real and imaginary terms: = (-22 + 42) + (-66 - 14)i

  5. Final result: = 20 - 80i

Therefore, the product of (-11 - 7i) and (2 + 6i) is 20 - 80i.

Key Points

  • Remember to distribute each term of the first complex number to both terms of the second complex number.
  • Replace i² with -1 whenever it appears in the multiplication.
  • Combine real and imaginary terms separately to express the final answer in the standard form a + bi.

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