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

Principle of Mathematical Induction

Principle of Mathematical Induction:-

<img src="principle of mathematical induction" alt="principle of mathematical induction">

we know that the first positive even integer is 2 = 2  \times 1
the second positive even integer is 4 =  {\rm{ }}2 \times 2

the third positive even integer is 6 = 2 \times 3
the fourth positive even integer is 8 = 2 \times 4


If we move using the same pattern then nth positive integer=2n Read more

How to Become a Good Learner in Classroom or in Online sessions

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

Positive Attitude- A positive attitude plays a very important part in improving our learning capacities.Actually, its the backbone of our learning capacities.If we believe that we can do it, we will surely be able to accomplish the work <img src="good learner.png" alt="good learner"> Read more

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 the 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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