Unformatted text preview: sible:
1). If a = 0 , then x = 0.
2). If a is a positive number, then its square root has two values: one positive and one negative; for example,
the equation x2 = 25 has the two roots: 5 and –5.
This is often written as the root with double sign before:
3). If a – a negative number, then the equation has no solution among known us positive and negative
numbers, because the second power of any number is a non-negative number (think over this!). But, if we
wish to receive solutions of the equation x2 = a also at negative values of a, we are obliged to introduce
the new kind numbers – imaginary numbers. So, a number is imaginary, if its second power is a negative
number. According to this definition of imaginary numbers we can define an imaginary unit as: Then, for the equation
x2 = – 25
we receive the two imaginary roots:
roots into our equation we’ll receive the identity. Check it, please! Substituting both these In contrast to imaginary numbers all the rest numbers (positive and negative, integers and fractional, rational
and irrational ones) are called real numbers. A sum of a real and an imaginary number is called a complex
number, and marked as:
Math I - 19 - Feel free to pass this on to your friends, but please don’t post it online.
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This note was uploaded on 07/21/2013 for the course UPCAT 2014 taught by Professor Otis during the Spring '13 term at University of the Philippines Diliman.
- Spring '13