complex

# complex - Appendix B 1 Complex Numbers P Danziger Some...

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Appendix B Complex Numbers P. Danziger 1 Some Useful Sets 1.1 The Empty Set Deﬁnition 1 The empty set is the set with no elements, denoted by φ . 1.2 Number Sets N = { 0 , 1 , 2 , 3 ,... } - The natural numbers. Z = { ..., - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 ,... } - The integers. Q = { x y | x Z y N + } - The rationals. R = ( -∞ , ) - The Real numbers. I = R - Q (all real numbers which are not rational) - The irrational numbers. C = { x + yi | x,y R } - The Complex numbers. Note: There are many real numbers which are not rational, e.g. π , 2 etc. 2 Complex Numbers 2.1 Introduction We can’t solve the equation x 2 + 1 = 0 over the real numbers, so we invent a new number i which is the solution to this equation, i.e. i 2 = - 1. Complex numbers are numbers of the form z = x + iy, where x,y R . The set of complex numbers is represented by C . Generally we represent Complex numbers by z and w , and real numbers by x,y,u,v , so z = x + iy, w = u + iv, z,w

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complex - Appendix B 1 Complex Numbers P Danziger Some...

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