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(−1−5i)⋅(1−2i)

less than a minute read Jun 17, 2024
(−1−5i)⋅(1−2i)

Multiplying Complex Numbers: (-1 - 5i) * (1 - 2i)

This article will guide you through the process of multiplying the complex numbers (-1 - 5i) and (1 - 2i).

Understanding Complex Numbers

Complex numbers are numbers of the form a + bi, where:

  • a is the real part.
  • b is the imaginary part.
  • i is the imaginary unit, where i² = -1.

Multiplication Process

To multiply complex numbers, we use the distributive property, just like with binomials.

  1. Expand: (-1 - 5i)(1 - 2i) = (-1 * 1) + (-1 * -2i) + (-5i * 1) + (-5i * -2i)

  2. Simplify: = -1 + 2i - 5i + 10i²

  3. Substitute i² with -1: = -1 + 2i - 5i + 10(-1)

  4. Combine real and imaginary terms: = (-1 - 10) + (2 - 5)i

  5. Final Result: = -11 - 3i

Therefore, (-1 - 5i) * (1 - 2i) = -11 - 3i.

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