Transcription of COMPLEX NUMBERS - Number theory
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COMPLEX NUMBERS - Number theory
chapter 5 COMPLEX 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}.8990 chapter 5.
Chapter 5 COMPLEX NUMBERS 5.1 Constructing the complex numbers One way of introducing the field C of complex numbers is via the arithmetic of 2×2 matrices.
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