(-5+3i)-(4-5i)

2 min read Jun 16, 2024
(-5+3i)-(4-5i)

Subtracting Complex Numbers: A Step-by-Step Guide

This article will guide you through the process of subtracting complex numbers, using the example of (-5 + 3i) - (4 - 5i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where:

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

Subtracting Complex Numbers

To subtract complex numbers, we follow these steps:

  1. Distribute the negative sign:

    • (-5 + 3i) - (4 - 5i) becomes -5 + 3i - 4 + 5i
  2. Combine the real terms:

    • (-5 - 4) + (3i + 5i)
  3. Combine the imaginary terms:

    • -9 + 8i

Therefore, the result of (-5 + 3i) - (4 - 5i) is -9 + 8i.

Key Points to Remember

  • When subtracting complex numbers, we subtract the real parts and the imaginary parts separately.
  • The imaginary unit 'i' remains unchanged during the subtraction process.

This example demonstrates a simple subtraction of complex numbers. You can apply the same principle to more complex problems involving multiple complex numbers.

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