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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
11th-12th Foundation

### Complex Numbers

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)

Properties of Complex Number Arithmetic

Complex number system is an extension of Real number system with inclusion of a new number i=sqrt(-1). The complex arithmetic has the properties mostly identical to real arithmetic. The additional features are related to modulus, argument, and conjugate.

Learn these in a simple-thought-process.

(click for the list of pages in the lesson)