Complex Numbers

Complex Numbers-

Complex numbers come into existence when the square of a number is negative because we know it very well that the square of a number will always be positive doesn’t matter whether the number is positive or negative.<img src="complex number world.jpg" alt="complex number world">

In cases like  {x^2} + 1 = 0 or  2{x^3} + 5x = 0 here, if we solve, we find the square of x=-1. We say that x is not real here. Generally, these types of cases are considered as Complex numbers. Complex numbers were first observed by mathematician Girolamo Cardano (1501-1575). In his book Ars Magna, he discussed the mechanics of complex numbers in details and thus he started Complex Algebra.

Standard form of Complex Numbers-

Complex numbers are defined as expressions of the form a + ib where a,b \in  R & i = \sqrt { - 1}

It is denoted by Z  i.e. z= a + ib.

‘a’  is called as real part of z= (Re z)

and ‘b’ is called as imaginary part of z =(Im z).

i or IOTA- iota is a unique symbol. it’s the ninth letter of Latin alphabet. It’s used to denote imaginary numbers whose square root is -1.
Click here to download the book “An Imaginary Tale The Story of i” a very interesting book on iota by Paul J. Nahin. Read more

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Every moment of our life offers something to learn.We should always be ready to grab the opportunity.In this post, I have tried to identify characteristics of a good learner in classroom as well as with online tutors

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How to represent irrational numbers on number line

irrational number

Representation of irrational numbers on the number line

Irrational numbers are the numbers which have a non terminating and non-repeating decimal expansion. They don’t have any fixed value so we can’t represent them directly on the number line. we have to use a few tricks for this

Before understanding representation of irrational numbers on number line first, we need to understand Pythagoras’ theorem
Pythagoras’ Theorem:: Over 2000 years ago there was an amazing discovery about triangles:
When a triangle has a right angle (90°) and squares are made on each of the three sides then the biggest square has the exact same area as the other two squares put together!

irrational numbers

pythagorus theorem

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