Complex Number System Arithmetic A complex number is an expression in the form: a + bi where a and b are real numbers. The symbol i is defined as √ 1. a is the real part of the complex number‚ and b is the complex part of the complex number. If a complex number has real part as a = 0‚ then it is called a pure imaginary number. All real numbers can be expressed as complex numbers with complex part b = 0. -5 + 2i 3i 10 real part –5; imaginary part 2 real part 0; imaginary part 3 real part 10; imaginary
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THE DIVINITY OF NUMBER: The Importance of Number in the Philosophy of Pythagoras by Br. Paul Phuoc Trong Chu‚ SDB Pythagoras and his followers‚ the Pythagoreans‚ were profoundly fascinated with numbers. In this paper‚ I will show that the heart of Pythagoras’ philosophy centers on numbers. As true to the spirit of Pythagoras‚ I will demonstrate this in seven ways. One‚ the principle of reality is mathematics and its essence is numbers. Two‚ odd and even numbers signify the finite and
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Real Numbers -Real Numbers are every number. -Therefore‚ any number that you can find on the number line. -Real Numbers have two categories‚ rational and irrational. Rational Numbers -Any number that can be expressed as a repeating or terminating decimal is classified as a rational number Examples of Rational Numbers 6 is a rational number because it can be expressed as 6.0 and therefore it is a terminating decimal. -7 ½ is a rational number because it can be expressed as -7.5 which is a
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The Number Devil The Number Devil - A Mathematical Adventure‚ by Hans Magnus Enzensberger‚ begins with a young boy named Robert who suffers from reoccurring nightmares. Whether he’s getting slurped up by a giant fish‚ sliding down an endless slide into a black hole‚ or falling into a raging river‚ his incredibly detailed dreams always seem to have a negative effect on him. Robert’s nightmares either frighten him‚ make him angry‚ or disappoint him. His one wish is to never dream again; however‚
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REAL NUMBERS Q.1 Determine the prime factorization of the number 556920. (1 Mark) (Ans) 23 x 32 x 5 x 7 x 13 x 17 Explanation : Using the Prime factorization‚ we have 556920 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13 x 17 = 23 x 32 x 5 x 7 x 13 x 17 Q.2 Use Euclid’s division algorithm to find the HCF of 210 and 55. (1 Mark) (Ans) 5 Explanation: 5 ‚ Given integers are 210 and 55 such that 210 > 55. Applying Euclid’s division leema to 210 and 55‚ we get 210 = 55 x 3 + 45 ………
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The Number Devil Prima Donna Numbers Prima- donna numbers is another name for prime numbers. Prima- donna numbers/ prime numbers can only be divided evenly by one and itself. In The Number Devil‚ the Number Devil does the prima-donna numbers from 0 to 50. I created a chart‚ just like in the number devil and figured out which ones are prima-donna numbers. The number 0 does not count because if you divide a number by 0 the answer will always be 0. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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Cardinal numbers: Definition‚ Examples Cardinal numbers We know that‚ the relation in sets defined by A~ B is an equivalence relation. Hence by fundamental theorem on equivalence relation‚ all sets are partitioned into disjoint classes of equivalent sets. Thus for any set A‚ equivalence class of A‚ [A] = { B | B ~ A } Result: - (1) [A] = [B] or [A] ∩ [B] = ∅ ‚ that is for any two sets‚ either they have same equivalence classes or totally disjoint equivalence classes.
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A rational number is a number that can be written as a ratio of two integers. The decimal of a rational number will either repeat or terminate. There is a way to tell in advance whether a rational number’s decimal representation will repeat or terminate. When trying to find a pattern in the relationship between rational numbers and their decimals‚ it is best to start with a list. A random list of rational numbers and their decimal values was made in order to find a pattern. The list included ½‚ 5/6
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plurals-------------------------------------------------------------------------------7 Irregular plurals from Latin and Greek------------------------------------------------7 Words better known in the plural-----------------------------------------------------10 Plurals of numbers-----------------------------------------------------------------------11 Plurals and units of measure----------------------------------------------------------11 Plurals of headless nouns--------------------------------------------------------------11
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Perfect numbers Mathematicians have been fascinated for millenniums by the properties and patterns of numbers. They have noticed that some numbers are equal to the sum of all of their factors (not including the number itself). Such numbers are called perfect numbers. A perfect number is a whole number‚ an integer greater than zero and is the sum of its proper positive devisors‚ that is‚ the sum of the positive divisors excluding the number itself. Equivalently‚ a perfect number is a number that is
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