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Introduction to Complex Numbers

Introduction to Complex Numbers

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Irrational Number Representation


 »  irrational numbers
    →  solutions of algebraic equations in real line
    →  eg: `sqrt(2)` is one solution of `x^2=2`


 »  irrational numbers are represented as numerical expressions
    →  eg: `3+4 root(3)(5)` is one solution of `((x-3)/4)^3 = 5`

Irrational Number Notation

plain and simple summary

nub

plain and simple summary

nub

dummy

Irrational numbers are represented as numerical expressions or with a symbol.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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This page reviews the representation of irrational numbers. The complex number notation is very similar to the representation of irrational numbers -- both are given as numerical expressions.


Keep tapping on the content to continue learning.
Starting on learning "Irrational Number Notation". ;; This page reviews the representation of irrational numbers. The complex number notation is very similar to the representation of irrational numbers -- both are given as numerical expressions.

Irrational numbers are 'numbers that cannot be represented as `p/q` and are on the number line.
The equation `x^2 = 2` has the solutions in irrational numbers. Which one in the following is the exact solution?

  • `+-1.4`
  • `+-1.41`
  • `+-1.414`
  • none of the above is the exact solution

The answer is 'None of these is the exact solution'.

What is the value of `x` in `x^2=2`?

  • `+-sqrt(2)`
  • the solution is given as a numerical expression
  • both the above

The answer is 'Both the above'. `sqrt(2)` is a numerical expression involving a square root symbol.

What is the solution to `(x-1)^2=2`?

  • `+-sqrt(2)+1`
  • the solution is given as a numerical expression
  • both the above

The answer is 'Both the above'. `sqrt(2)+1` is a numerical expression involving a square root symbol and an addition.

What is the ratio of circumference to diameter of a circle? Find the exact value in the following.

  • `22/7`
  • `3.14`
  • `pi`

The answer is '`pi`'. The number is represented with a symbol or a letter.

is `pi` a rational number?

  • No, `pi` is an irrational number
  • yes, `pi` is a rational number

The answer is 'No, `pi` is an irrational number'. This particular irrational number is represented with a letter `pi`.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Representation of Irrational Numbers : Irrational numbers are represented with numerical expressions (eg: `root(3)(4)+3`) or with symbols (eg: `pi, e`)



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Is `e` (a constant, that is base of natural logarithm) a rational number?

  • No. `e` is an irrational number
  • Yes. `e` is a rational number

The answer is 'No. `e` is an irrational number'

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Progress

Irrational numbers are 'numbers that cannot be represented as p by q and are on the number line'. ;; The equation x squared = 2 has the solutions in irrational numbers. Which one in the following is the exact solution?
plus;minus;1
plus or minus 1 point 4
point;4
plus or minus 1 point 4 one
4 1 4
plus or minus 1 point 4 one four
none;above;exact;solution
none of the above is the exact solution
The answer is 'None of these is the exact solution'.
What is the value of x in x squared equals 2?
plus;minus;square;root;2
plus or minus square root of 2
solution;numerical;expression
the solution is given as a numerical expression
both;above
both the above
The answer is 'Both the above'. ;; square root of 2 is a numerical expression involving a square root symbol.
what is the solution to x minus 1 squared equals 2?
plus;minus;square;root
plus or minus square root of 2 plus 1
solution;numerical;expression
the solution is given as a numerical expression
both;above
both the above
The answer is 'Both the above'. Square root of 2 plus 1 is a numerical expression involving a square root symbol and an addition.
What is the ratio of circumference to diameter of a circle? Find the exact value in the following.
22;7;by
22 by 7
3;point;1;4
3 point one 4
pi;pie
pi
The answer is ' pi '. The number is represented with a symbol or a letter.
is pi a rational number?
no;irrational
No, pi is an irrational number
yes;rational
yes, pi is a rational number
The answer is 'No, pi is an irrational number'. This particular irrational number is represented with a letter pi .
Irrational numbers are represented as numerical expressions or with a symbol.
Representation of Irrational Numbers : Irrational numbers are represented with numerical expressions. ;; for example third root of 4 plus 3 ;; or with symbols ;; for example pi and e.
Is e ;; a constant that is base of natural logarithm ;; a rational number?
no;irrational
No. e is an irrational number
yes;s;rational
Yes. e is a rational number
The answer is 'No. e is an irrational number'

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