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Thought-Process to Discover Knowledge
Welcome to the novel approach to understanding complex numbers: it completely changes the way complex numbers are thought-about and learned.
• Irrational numbers are numerical expressions, eg: `2+root(5)(3)`
» Complex numbers are numerical expressions too.
• Irrational numbers do not have a standard form. They are expressed as numerical expressions, with some having many terms. eg: `2+ root(2)(2)-3xx root(3)(5)`
» Similar to irrational numbers, the direct extension is to express complex numbers as numerical expressions. eg: `x^3=1` has `3` solutions, `(root(3)(1))_(1st)`, `(root(3)(1))_(2nd)`, `(root(3)(1))_(3rd)`
» But, Any complex number is given in a standard form `a+ib`, because of Euler Formula `re^(i theta)``= r(cos theta + i sin theta)`
How so? Go through the first few lessons to get the astoundingly new perspective of complex numbers.
(click for the list of lessons in this topic)
Algebra of Complex Numbers
Algebra of complex numbers details out the operations addition, subtraction, multiplication , division, conjugate, and exponent.
The algebra of complex numbers is quite easy to understand in abstraction. This topic goes beyond and explains the application context.
Learn these in a simple-thought-process.