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.

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

Subtract the following complex numbers: $(5 + 3i) - ( 2 + 7i) $

Step 1

This problem is very similar to example 1


Distribute the negative

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

Step 2

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

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

Step 3

Combine the like terms and simplify

$$3 - 4i$$

Problem 2

Subtract the following 2 complex numbers $(9 + 11i) - (3 + 5i) $

Step 1

This problem is very similar to example 1


Distribute the negative

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

Step 2

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

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

Step 3

Combine the like terms and simplify

$$ 6 + 6i$$

Problem 3

Subtract the complex numbers below $(12 + 14i) - (3 -2i)$

Step 1

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


Distribute the negative

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

Step 2

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

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

Step 3

Combine the like terms and simplify

$$ 9 + 16i $$

Problem 4

Subtract the following 2 complex numbers $(6 - 13i) - (12 + 8i)$

Step 1

This problem is very similar to example 1


Distribute the negative

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

Step 2

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

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

Step 3

Combine the like terms and simplify

$$ -6 + -21i $$

Problem 5

Subtract the following complex numbers $(-2 - 15i) - (-12 + 13i)$

Step 1

Distribute the negative

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

Step 1

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

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

Step 1

Combine the like terms and simplify

$$ 10 - 28i $$


Ultimate Math Solver (Free)

Free Algebra Solver ... type anything in there!