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# How To Add 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
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
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
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
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
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

$$-14 + 2i$$