1. OPERATIONS WITH COMPLEX NUMBERS PRE-CALCULUS

2. IMAGINARY AND COMPLEX NUMBERS The imaginary unit i is defined as the principle square root of -1. i =

3. IMAGINARY AND COMPLEX NUBMERS The first eight powers of i are listed below: Do you notice a pattern?

4. POWERS OF I To find the value of i n, let R be the remainder when n is divided by 4.

5. POWERS OF I Try these: 1. i 53 2. i -18

6. POWERS OF I A complex number is a number that can be written in the standard form a + bi, where a is the real part and the real number b is the imaginary part. If a ≠ 0 and b = 0, the complex number is a +0 i, or the real number a. Therefore, all real numbers are also complex numbers. If b ≠ 0 the complex number is known as an imaginary number. If a = 0 and b ≠ 0, such as 4 i or -9 i, the complex number is a pure imaginary number.

7. ADDING & SUBTRACTING COMPLEX NUMBERS Simplify: 1.) (5 – 3 i ) + (-2 + 4 i )2. (10 – 2 i ) – (14 – 6 i )

8. MULTIPLYING COMPLEX NUMBERS Simplify: 1. (2 – 3 i ) (7 – 4 i )2. (4 + 5 i ) (4 – 5 i )

9. RATIONALIZE A COMPLEX EXPRESSION Simplify 1. (5 – 3 i ) ÷ (1 – 2 i )

10. ASSIGNMENT Pg. P8 # 1-32 EVEN