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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)
Complex Plane and Polar Form
Complex number `a+i b` is equivalently an ordered pair `(a,b)` which can be abstracted to represent a 2D plane. This is named after the mathematician JR Argand as Argand Plane or complex plane with real and imaginary axes.
Complex numbers, having abstracted to a complex plane, are represented in polar form.
Learn these in a simple-thought-process.