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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)

Introduction to Complex Numbers

This lesson provides the astoundingly new perspective of complex numbers.

Irrational numbers were introduced as solution to algebraic equations similar to x^2=2. Similarly, complex numbers are introduced as solutions to algebraic equations similar to (x-a)^2=-b.

At the end of this topic, the generic form of complex numbers is proven to be a+ib.

(click for the list of pages in the lesson)

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.

(click for the list of pages in the lesson)

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.

(click for the list of pages in the lesson)

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)