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:
-
Distribute the negative sign:
- (-5 + 3i) - (4 - 5i) becomes -5 + 3i - 4 + 5i
-
Combine the real terms:
- (-5 - 4) + (3i + 5i)
-
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.