How to Add and Subtract Complex Numbers? (+FREE Worksheet!)

Learn more about complex numbers and how to add and subtract them using the following step-by-step guide.

How to Add and Subtract Complex Numbers? (+FREE Worksheet!)

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Step by step guide to add and subtract the complex numbers

  • A complex number is expressed in the form \(a+bi\), where \(a\) and \(b\) are real numbers, and \(i\), which is called an imaginary number, is \(a \) solution of the equation \(x^2=-1\)
  • For adding complex numbers: \((a+bi)+(c+di)=(a+c)+(b+d)i\)
  • For subtracting complex numbers: \((a+bi)-(c+di)=(a-c)+(b-d)i\)

Adding and Subtracting Complex Numbers – Example 1:

Solve: \(10+(-5-3i)-2\)

Solution:

Remove parentheses: \(10+(-5-3i)-2=10-5-3i-2\)
Combine like terms: \(10-5-2=10-7=3\)

Then: \(10-5-3i-2=3-3i\)

Adding and Subtracting Complex Numbers – Example 2:

Solve: \(-3+(4i)+(9-2i)\)

Solution:

Remove parentheses: \(-3+(4i)+(9-2i)=-3+4i+9-2i\)
Combine like terms: \(-3+9=6 , 4i- 2i=2i\)

Then: \(-3+4i+9-2i=6+2i\)

Adding and Subtracting Complex Numbers – Example 3:

Solve: \((-8+2i)+(-8+6i)\)

Solution:

Remove parentheses: \((-8+2i)+(-8+6i)=-8+2i-8+6i\)
Combine like terms: \(-8-8=-16 , 2i+6i=8i\)
Then: \(-8+2i-8+6i=-16+8i\)

Adding and Subtracting Complex Numbers – Example 4:

Solve: \((6-3i)-(-8-7i)\)

Solution:

Remove parentheses by multiplying the negative sign to the second parenthesis: \((6-3i)-(-8-7i)=6-3i+8+7i\)
Combine like terms: \(6+8=14 , -3i+7i=4i\)

Then: \(6-3i+8+7i= 14+ 4i\)

Exercises for Adding and Subtracting Complex Numbers

Simplify.

  • \(\color{blue}{– 8 + (2i) + (– 8 + 6i)}\)
  • \(\color{blue}{12 – (5i) + (4 – 14i)}\)
  • \(\color{blue}{– 2 + (– 8 – 7i) – 9}\)
  • \(\color{blue}{(– 18 – 3i) + (11 + 5i)}\)
  • \(\color{blue}{(3 + 5i) – (8 + 3i)}\)
  • \(\color{blue}{(8 – 3i) – (4 + i)}\)

Download Adding and Subtracting Complex Numbers Worksheet

  • \(\color{blue}{– 16 + 8i}\)
  • \(\color{blue}{16 – 19i}\)
  • \(\color{blue}{–19 – 7i}\)
  • \(\color{blue}{–7 + 2i}\)
  • \(\color{blue}{-5 + 2i}\)
  • \(\color{blue}{4 – 4i}\)

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