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(3-4i)+(-7-8i) In Simplest Form

2 min read Jun 16, 2024
(3-4i)+(-7-8i) In Simplest Form

Adding Complex Numbers: (3 - 4i) + (-7 - 8i)

This article will guide you through adding the complex numbers (3 - 4i) and (-7 - 8i) to arrive at the simplest form.

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 (i² = -1)

Adding Complex Numbers

Adding complex numbers is straightforward. We simply add the real parts and add the imaginary parts separately.

Solving the Problem

  1. Identify the real and imaginary parts:

    • (3 - 4i): Real part = 3, Imaginary part = -4
    • (-7 - 8i): Real part = -7, Imaginary part = -8

  2. Add the real parts: 3 + (-7) = -4

  3. Add the imaginary parts: (-4) + (-8) = -12

  4. Combine the results: -4 - 12i

Final Answer

Therefore, the sum of (3 - 4i) and (-7 - 8i) in its simplest form is -4 - 12i.

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