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How To Add Complex Numbers

Worksheet with answer key on adding and subtracting complex numbers
Complex Number Calculator

How do you add Complex Numbers

Video Tutorial on Adding Complex Numbers

An Example

Calculate $$ (5 + 2i ) + (7 + 12i)$$

Step 1

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

$$ \blue{ (5 + 7) }+ \red{ (2i + 12i)}$$

Step 2

Combine the like terms and simplify

$$ 12 + 14i$$

Practice Problems

Problem 1

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

Step 1

This problem is very similar to example 1

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

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

Step 2

Combine the like terms and simplify

$$ 7 + 10i$$

Problem 2

Add the following 2 complex numbers: $$ (9 + 11i) + (3 + 5i)$$

Step 1

This problem is very similar to example 1

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

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

Step 2

Combine the like terms and simplify

$$12 + 16i$$

Problem 3

Add the following 2 complex numbers: $$ (12 + 14i) + (3 - 2i) $$

Step 1

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

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

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

Step 2

Combine the like terms and simplify

$$15 + 12i $$

Problem 4

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

Step 1

This problem is very similar to example 1 with the added twist that we have a negative number in there (-13i).

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

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

Step 2

Combine the like terms and simplify

$$ 18 - 5i$$

Problem 5

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

Step 1

This problem is very similar to example 1 with the added twist that we have a negative number in there (-13i).

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

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

Step 2

Combine the like terms and simplify

$$ -14 + 2i $$

Worksheet with answer key on adding and subtracting complex numbers
Complex Number Calculator
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