We are going to see how we can use the rules for adding in the real number system to add complex numbers. Recall that Complex Numbers are written in the form of a + bi. Therefore, we are going to add "like terms" together by treating a like a constant (a number by itself), and b like a coefficient (the number in front of a variable), and i like a variable ( a letter used to represent a number).

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

= (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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