Some of the solution sets for quadratic equations in the next sections in this chapter will contain complex numbers such as − 4 + − 12 2 and − 4 − − 12 2 . We can simplify the first number as follows. − 4 + − 12 2 = − 4 + i 12 2 = − 4 + 2 i 3 2 = 2 ( 2 + i 3 ) 2 = − 2 + i 3 Simplify each of the following complex numbers. (Objective 3) (a) − 4 − − 12 2 (b) 6 + − 24 4 (c) − 1 − − 18 2 (d) − 6 + − 27 3 (e) 10 + − 45 4 (f) 4 − − 48 2

Some of the solution sets for quadratic equations in the next sections in this chapter will contain complex numbers such as − 4 + − 12 2 and − 4 − − 12 2 . We can simplify the first number as follows.

− 4 + − 12 2 = − 4 + i 12 2 = − 4 + 2 i 3 2 = 2 ( 2 + i 3 ) 2 = − 2 + i 3

Simplify each of the following complex numbers.

(Objective 3)

(a) − 4 − − 12 2	(b) 6 + − 24 4
(c) − 1 − − 18 2	(d) − 6 + − 27 3
(e) 10 + − 45 4	(f) 4 − − 48 2