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(4-3i)(-7-2i)

less than a minute read Jun 16, 2024
(4-3i)(-7-2i)

Multiplying Complex Numbers: (4 - 3i)(-7 - 2i)

This article will guide you through the process of multiplying two complex numbers: (4 - 3i) and (-7 - 2i).

Understanding Complex Numbers

A complex number is a number 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 (i² = -1)

Multiplying Complex Numbers

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

  1. Expand the product: (4 - 3i)(-7 - 2i) = 4(-7 - 2i) - 3i(-7 - 2i)

  2. Distribute: = -28 - 8i + 21i + 6i²

  3. Simplify using i² = -1: = -28 - 8i + 21i - 6

  4. Combine real and imaginary terms: = (-28 - 6) + (-8 + 21)i

  5. Final answer: = -34 + 13i

Therefore, the product of (4 - 3i) and (-7 - 2i) is -34 + 13i.

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