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How To Add Complex Numbers

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

$$ -14 + 2i $$


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