## Subtracting Complex Numbers: (5-i)-(3-2i)

This article will guide you through the process of subtracting complex numbers, using the example of **(5 - i) - (3 - 2i)**.

### Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form **a + bi**, where *a* and *b* are real numbers, and *i* is the imaginary unit, defined as the square root of -1.

### Subtracting Complex Numbers

Subtracting complex numbers is similar to subtracting binomials. We simply subtract the real and imaginary components separately.

**Step 1: Distribute the negative sign**

The negative sign in front of the second complex number needs to be distributed to both its terms:

(5 - i) + **(-1) * (3 - 2i)**

This becomes:

(5 - i) + (-3 + 2i)

**Step 2: Combine the real and imaginary terms**

Now, group the real terms together and the imaginary terms together:

**(5 - 3) + (-1 + 2)i**

**Step 3: Simplify**

Finally, perform the simple addition:

**2 + i**

### Conclusion

Therefore, the result of subtracting (3 - 2i) from (5 - i) is **2 + i**.

By following these steps, you can confidently subtract any two complex numbers.