# Adding Complex Numbers

**like a**

*a***constant**(a number by itself), and

**like a**

*b***coefficient**(the number in front of a variable), and

**like a**

*i***variable**( a letter used to represent a number).

Let's refresh our memory about addition in the real number system:

(2+3x) + (-5 + 8x)

= (2 + -5) + (3x + 8x) group like terms

= -3 + 11xsimplify

= (2 + -5) + (3x + 8x) group like terms

= -3 + 11xsimplify

Now let's look at some examples. (Be sure that your final answer is in

**a + bi**form.)

- 2i + 5i
- 2i + 5iadd the coefficients of the "like terms"

= 7isimplify

- (3 + 4i) + (-2 + 3i)
- (3 + 4i) + (-2 + 3i)identify like terms.

= [3 +(-2)] + [4i + 3i]group like terms - constants first

= 1+7isimplify by adding the "constants" together and then the "coefficients" of i.

- (7i) + (4 = 2i)
- (7i) + (4 - 2i)identify constants and coefficients of i

= 4 + (7i + -2i)group like terms - constants first

= 4 + 5isimplify by adding the "constants" together and then the "coefficients" of i.

As you can see Adding Complex Numbers is the same as adding in the Real Number system. All you have to do is add the constants, add the coefficients of i and then write your answer in the form of a + bi.

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