January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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Definition A complex number is an ordered pair z 5 ðx; yÞ of real numbers x and y.
We call x the real art of z and y the imaginary part, and we write Re z 5 x,Imz 5 y.
Example: z 5 5 1 2i.
−2 + 3i
1 + 2i
π + 1.5i
Real number line
Imaginary number line
√
2
+ i
/
2
−√
2
+ i
−10123−2
−2 − i
3 − i
−i
−2i
−3i
1 − πi
−1.5 − ei
−3
3i
2i
i
2.2 Fundamental Properties of Numbers
Linear inequalities: Linear inequalities in the real number system are the statements,
such as a . b, a , b, a $ b, a # b,wherea & b are real numbers.
Definition
1. a . b3a 2 b . 0. Example: 5 . 335 2 3 5 2 . 0
2. a , b3b . a. Example: 5 , 935 2 9 524 , 0
3. a $ b3either a . b or a 5 b
4. a # b3either a , b
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