Adding and Subtracting Complex Numbers

Adding and Subtracting Complex Numbers

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

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: \((a+bi)-(c+di)=(a-c)+(b-d)i\)

Example 1:

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

Solution:

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

Example 2:

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

Solution:

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

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: \(-8-8+2i+6i=-16+8i\)

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

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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