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10 Part I: Technical Mathematics
Every positive number has a square root. For example, using a calculator we can
determine that
Part I.A
Imaginary Numbers
54. 3 = 7. 369.
The square root of a negative number does not exist on the real number line.
Rather, the imaginary number i is defined as the square root of –1. The result is
written in terms of i. For example,
25 = – 1× 25 = 1 × 25 = 5i.
Exponents
A whole number exponent indicates how many times a number is multiplied by
itself. For example,
ORDER OF OPERATIONS
7× 7 = 7
3
7× 7× 7 = 7 .
The order of operations can be remembered by using the mnemonic device of
PEMDAS, or Please Excuse My Dear Aunt Sally, which stands for Parentheses,
Exponents, Multiplication, Division, Addition, and Subtraction. As an illustration,
the expression
is correctly evaluated as follows:
FACTORIALS
6× 4+ ( 9
1) ÷ 2
5 2
2 2
6× 4+ ( 9
1)÷ 2 5 = 6× 4+ 8 ÷ 2
5 P
2
= 6× 4+ 8÷ 2
25 E
= 24+
8 ÷ 2
25 M
= 24+ 4 25 D
= 28
25 A
= 3
S
A factorial is a mathematical operation denoted by an exclamation point (!), and is
evaluated in the following manner: