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OPERAT
IONS W
ITH
COMPLEX N
UMBERS
PR
E- C
AL C
UL U
S
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