• services@thehomeworkhelp.co.uk
Call Us Now: 8185279935
Call Us Now: 8185279935
Homework Help
Homework Help
Homework Help
View Details
Homework Help
Assignment Help
Homework Help
Assignment Help
View Details
Assignment Help
Online Tutoring
Online Tutoring
Online Tutoring
View Details
Online Tutoring
Home » Math Homework Help » Algebra Homework Help » Complex Numbers Representation
Complex Numbers Representation
Let CR be the set of complex numbers of the type (a, 0)

i.e. CR = {(a, 0) | a R}

Surely, CR ⊂ C. Now, it is possible to set up a one-one correspondence between the elements of CR and the elements of R, the set of real numbers.

Let ƒ : R CR be defined as

ƒ(a) = (a, 0),            ∀ a R

Let us now show that the mapping ƒ has a composition preserving property.

i.e. (i) ƒ(a + b) = (a + b, 0) = (a, 0) + (b, 0) = ƒ(a) + ƒ(b), ∀ a, b R

(ii) ƒ(ab) = (ab, 0) = (a, 0) (b, 0) = ƒ(a). ƒ(b), ∀ a, b R


Hence under the mapping ƒ, the addition and multiplication composition are preserved and also it associates to each real number R, whose first coordinate is a and the second coordinate is zero.

Let z = (a, b) C ; then

(a, b) = (a, 0) + (0, b)

= (a, 0) + (0, 1) (b, 0)                              (1)


Clearly, (0, 1) (0, 1) = (-1, 0) - -1     [by the above form ƒ : CR  - R]

Let us denote (0, 1) by i; then

i2 = -1,

and from (1), we get

z = (a, b) = (a, 0) + (b, 0) = a + ib

Hence z = a + ib,

which is the usual notion of a complex number.

In this complex number, “a” is called the real part of complex number (a, b, and “b” is called the imaginary part of the complex number (a, b). A complex number is called purely real if its imaginary part is zero and it is called purely imaginary if its real part is zero but its imaginary part is not zero.

Services: - Complex Numbers Representation Homework | Complex Numbers Representation Homework Help | Complex Numbers Representation Homework Help Services | Live Complex Numbers Representation Homework Help | Complex Numbers Representation Homework Tutors | Online Complex Numbers Representation Homework Help | Complex Numbers Representation Tutors | Online Complex Numbers Representation Tutors | Complex Numbers Representation Homework Services | Complex Numbers Representation



Submit Your Query ???
Topics
Real Number Absolute Value Addition Of Matrices Square Matrix Adjoint Algebraic Structures Alternating Series Linear Equations Determinants Archimedean Real Numbers Binary Operation Binary Relation In A Set Bounded, Unbounded Sets Cauchy Root Test Caylay Hamiltion Theorem Circular Permutation Common Roots Complex Numbers Complex Number Conjugate Conjugate Of A Matrix Constant Sequences Convergence Of A Sequence Cosets Cubic, Biquadratic Equations De Moivre Theorem Real Number Denseness Order 3 Determinants Differences Of Matrices Direct Sum Of Vector Subspaces Eigen Vector Elementary Matrices Matrix Elem. Transformations Equal Matrices Equal Roots Two Permutations Equity Equivalent Matrices Trigonometry Function Expansion Field Function Algebra Fundamental Theorem Gaussian Integer Geometric Series Group Ideals Quantity Increasing Roots Infinite Series Convergent Integers Inverse Of Square Matrix Inverses Of Elementary Matrices Iota, Imaginary Numbers Left-Right Identity Sequence Limit Points Linear Combination Vectors Span Linear Dependence, Independence Linear Homogeneous Equations Two Subspaces Linear Sum Matric Polynomial Matrix Linear Equation Matrix Inverse Matrix Multiplication Matrix Scalar Multiplication Method Of Difference Minors And Co-factors Multiplication Modulo P Normal Sub-Group Normalizer Or Centalizer Orbit Of Permutation Peano Axioms Permutation Function Pigeon Hole Principle Matrices Integral Powers Mathematical Induction Principal Two Determinants Product Two Permutations Product Properties Of Modulus Rank Of A Matrix Rational Numbers Rational, Integral Polynomial Reciprocal Roots Relation Of Sets Rings Of A Set Row By Column Matrix Sequence Series Series Of Positive Terms Series Partial Sum Sequence Subrings Sum Of A Series Cosine Series Sum Sum Of Sine Series Symmetric/Skew Symm. Matrices Roots Symmetric Functions Symmetric Set Degree N Synthetic Division Transformation In General Transformations Of Equations Transpose Of A Matrix Matrix Transposed Conjugate Transposition Complex Numbers Representation Vector Space Vector Sub-spaces Whole Numbers
To book a free session write to:- tutoring@thehomeworkhelp.co.uk or call 8185279935