The Complex Plane, Relations, Functions

John Mac Sheridan Nerney
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John Mac Sheridan Nerney: Mathematics

Chapter Chapter 1 in An Introduction to Analytic Functions, 2020, pp 5-10 from Springer

Abstract: Abstract A complex number Complex number is an ordered pair of real numbers. If each of (a, b) and (c, d) is a complex number then addition and multiplication are defined on the set of complex numbers in the following way: ( a , b ) + ( c , d ) = ( a + c , b + d ) ( a , b ) ( c , d ) = ( a c − b d , a d + b c ) $$\displaystyle \begin {array}{c} (a,b) + (c,d) = (a+c,b+d)\\ (a,b) (c,d)=(a c-b d, a d+b c) \end {array} $$ The set of all complex numbers is denoted by ℂ $$\mathbb C$$ ℂ $$\mathbb C$$ . The symbol i i is used to denote the complex number (0, 1).

Date: 2020
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DOI: 10.1007/978-3-030-42085-7_2

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