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# Subtracting Complex Numbers

## Example, tutorial and practice

### Video Tutorial on Subtracting Complex Numbers

Note: The second half of the video focuses on subtracting complex numbers so if you already understand adding just skip to the middle.

### An Example

##### Example 1

Let's subtract the following 2 complex numbers

$(8 + 6i ) \red{-}(5 + 2i)$

Step 1

Distribute the negative

$$(8 + 6i ) + (\red{-}5 \red{-}2i)$$

Step 2

Group the real part of the complex number and the imaginary part of the complex number.

$$(8 + -5) + (6i + -2i)$$

Step 3

Combine the like terms and simplify

$$3 + 4i$$

### Practice Problems

##### Problem 1
Step 1

This problem is very similar to example 1

Destribute the negative.

$$(5 + 3i ) + (\red{-}2 \red{-} 7i)$$

Step 2

Group the real parts of the complex numbers and the imaginary parts of the complex numbers.

$$(5 + -2) + (3i + -7i)$$

Step 3

Combine the like terms and simplify

$$3 - 4i$$

##### Problem 2
Step 1

This problem is very similar to example 1

Destribute the negative.

$$(9 + 11i ) + (\red{-}3 \red{-}5i)$$

Step 2

Group the real parts of the complex numbers and the imaginary parts of the complex numbers.

$$(9 + -3) + (11i + -5i)$$

Step 3

Combine the like terms and simplify

$$6 + 6i$$

##### Problem 3
Step 1

This problem is very similar to example 1 with the added twist that we have a negative number in there $$-2i$$.

Destribute the negative.

$$(12 + 14i ) + (\red{-}3 + 2i)$$

Step 2

Group the real parts of the complex numbers and the imaginary parts of the complex numbers.

$$(12 + -3) + (14i + 2i)$$

Step 3

Combine the like terms and simplify

$$9 + 16i$$

##### Problem 4
Step 1

This problem is very similar to example 1

Destribute the negative.

$$(6 - 13i) + (\red{-}12 \red{-}8i)$$

Step 2

Group the real parts of the complex numbers and the imaginary parts of the complex numbers.

$$(6 + -12) + (-13i + -8i)$$

Step 3

Combine the like terms and simplify

$$-6 + -21i$$

##### Problem 5
Step 1

This problem is very similar to example 1

Destribute the negative.

$$(-2 - 15i) + (12 \red{-} 13i)$$

Step 2

Group the real parts of the complex numbers and the imaginary parts of the complex numbers.

$$(-2 + 12) + (-15i - 13i)$$

Step 3

Combine the like terms and simplify

$$10 - 28i$$