How to Add and Subtract Complex Numbers

How to Add and Subtract Complex Numbers

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

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

Adding and Subtracting Complex Numbers – Example 2:

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

Solution:

Remove parentheses: \(-3+(4i)+(9-2i)→-3+4i+9-2i\)
Group like terms: \(-3+4i+9-2i→6+2i\)

Adding and Subtracting Complex Numbers – Example 3:

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

Solution:

Remove parentheses: \((-8+2i)+(-8+6i)=-8+2i-8+6i\)
Group like terms: \(-8+2i-8+6i→-8-8+2i+6i\)
Add similar terms: \(-8-8+2i+6i=-16+8i\)

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

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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