COMPLEX NUMBERS - Number theory

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Chapter 5COMPLEX Constructing the COMPLEX numbersOne way of introducing the fieldCof COMPLEX NUMBERS is via the arithmeticof 2 2 COMPLEX Number is a matrix of the form x yyx ,wherexandyare real NUMBERS of the form x00x are scalar matrices and are calledrealcomplex NUMBERS and are denoted by the symbol{x}.The real COMPLEX NUMBERS {x}and{y}are respectively called therealpartandimaginary partof the COMPLEX Number x yyx .The COMPLEX Number 0 11 0 is denoted by the have the identities x yyx = x00x + 0 yy0 = x00x + 0 11 0 y00y ={x}+i{y},i2= 0 11 0 0 11 0 = 1 00 1 ={ 1}.8990CHAPTER 5. COMPLEX NUMBERSComplex NUMBERS of the formi{y}, whereyis a non zero real Number , arecalledimaginary two COMPLEX NUMBERS are equal, we can equate their real andimaginaryparts:{x1}+i{y1}={x2}+i{y2} x1=x2andy1=y2,ifx1, x2, y1, y2are real NUMBERS . Noting that{0}+i{0}={0}, gives theuseful special case is{x}+i{y}={0} x= 0 andy= 0,ifxandyare real sum and product of two real COMPLEX NUMBERS are also real complexnumbers:{x}+{y}={x+y},{x}{y}={xy} .

90 CHAPTER 5. COMPLEX NUMBERS Complex numbers of the form i{y}, where y is a non–zero real number, are called imaginary numbers. If two complex numbers are equal, we can equate their real and imaginary

  Number, Theory, Complex, Complex number, Complex numbers number theory, Complex numbers complex numbers