4.5 Inverse Quadratics – Complex Numbers

Ex 1 Find the inverse of

(a) y = 2x² – 1 (b) y = 3(x – 2)² – 2

Ex 2 Review of Operations with Radicals

Simplify

(a) (b) (c) (d)

Multiply

(a) (b)

Complex Numbers

All throughout math education, it has been said that there is no solution in the real numbers to negative square roots. This is accurate but people often misinterpret this to mean there is no solution at all. To solve this problem, there was a new number system invented-the complex number system.

The imaginary unit, , is the basis for the complex number system. or

Ex 3 Simplify

(a) (b) (c)

Ex 4 Multiply

(a) (b) (c)

Complex Numbers take the form a + bi. They are called are called complex because they are composed of a real component (a) and an imaginary component (bi).

Ex 5 Simplify

(a) (b)

Grade 11 Book

p. 216# 10, 12, 16a

p. 106# 1-9odd, 15