Polar Form of complex numbers-
In the previous post, we discussed the basics of complete numbers.This is the second and final post on the complex numbers.here we shalll discuss, polar form of complex numbers
We consider complex numbers like vectors and every vector must have some magnitude and a certain direction. If we write a complex number in form of a point in the Cartesian plane/ordered a pair like x+iy=(x,y) then the distance of this point from the origin (0,0) is equal to the magnitude of our complex number while the angle it’s making with x-axis will show it’s direction.
In the above right triangle, using Pythagoras theorem Read more
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.
In cases like or 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 R & i =
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:-
we know that the first positive even integer is 2 = 2 1
the second positive even integer is 4 =
the third positive even integer is 6 = 23
the fourth positive even integer is 8 = 24
If we move using the same pattern then nth positive integer=2n Read more