OPERATIONS WITH COMPLEX NUMBERS PRE-CALCULUS. IMAGINARY AND COMPLEX NUMBERS The imaginary unit i is...

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IMAGINARY AND COMPLEX NUMBERS

The imaginary unit i is defined as the principle square root of -1.

i = 1

IMAGINARY AND COMPLEX NUBMERS

The first eight powers of i are listed below:

Do you notice a pattern?

POWERS OF I

To find the value of in, let R be the remainder when n is divided by 4.

POWERS OF I

Try these:

1. i 53 2. i -18

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 +0i, 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 4i or -9i, the complex number is a pure imaginary number.

ADDING & SUBTRACTING COMPLEX NUMBERS Simplify:

1.) (5 – 3i) + (-2 + 4i) 2. (10 – 2i) – (14 – 6i)

MULTIPLYING COMPLEX NUMBERS

Simplify:

1. (2 – 3i) (7 – 4i) 2. (4 + 5i) (4 – 5i)

RATIONALIZE A COMPLEX EXPRESSION

Simplify

1. (5 – 3i) ÷ (1 – 2i)

ASSIGNMENT

Pg. P8 # 1-32 EVEN