Algebra, part IV- introductory number theory, complex numbers
This series of lessons is designed to help you learn, or review, the fundamentals of algebra. This lesson covers some number theory concepts, and introduces complex numbers.
Algebra opens the door to many other
areas in mathematics. Number theory and complex analysis are
great examples. Let's see what they're all
about.
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First of all- division and
mods division algorithm tells us that any number x can be divided by a number y such that We can also write this division statement as |
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Now comes the fun part-
primes!
A prime number is a number which has only 2 positive factor- 1 and itself. 2 is a prime number, as are 3,5,7,11,13,17,19,23 and so on and so forth. Every number that isn't prime is called a composite number.
According to a theory by Euclid (an old-school
mathematician who did tons of cool work) and similar theories by
other people (a respectful number of whom were Chinese), every
number factors into a unique set of primes. For example,
, and
no other number equals
.
This is the basis for Number Theory, which
obviously involves much more complex stuff. But I think in terms
of algebra, knowing the basics is enough. And speaking of complex
stuff…
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Introducing: complex numbers, and
"i" We've already seen that most numbers you know are real, and rational. For example, But here's the kick - what do we do with stuff like |
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We turn to complex numbers. These are numbers that include the number You should also note that if p<>. And now you're ready to solve any quadratic equation that comes your way. With the algebraic tools you've acquired, you can now write equations, simplify expressions by factoring and expanding, and solve these equations, whether the solutions are real or imaginary. |
And as always…
Thanks for reading this Welcome to
Algebra Lesson!
Click Here for Algebra-part-ii
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