File - PROJECT MATHS REVISION
... let the imaginary parts equal to each other, therefore creating two equations. Example 1 If a bi c di Then we can say that a c and b d Please note, that when equating complex numbers, we never use the i part of the questions; we just use the numbers in front of the is (the coefficients). E ...
... let the imaginary parts equal to each other, therefore creating two equations. Example 1 If a bi c di Then we can say that a c and b d Please note, that when equating complex numbers, we never use the i part of the questions; we just use the numbers in front of the is (the coefficients). E ...
Problem Set 3
... MATH 104: INTRODUCTORY ANALYSIS SPRING 2008/09 PROBLEM SET 3 Unlike the previous problem set, in this one you will need to prove your claims rigorously. 1. (a) Prove Bernoulli’s inequality: (1 + x)n ≥ 1 + nx for every real number x ≥ −1 and every n ∈ N. (b) Define the sequence (an )n∈N and (bn )n∈N ...
... MATH 104: INTRODUCTORY ANALYSIS SPRING 2008/09 PROBLEM SET 3 Unlike the previous problem set, in this one you will need to prove your claims rigorously. 1. (a) Prove Bernoulli’s inequality: (1 + x)n ≥ 1 + nx for every real number x ≥ −1 and every n ∈ N. (b) Define the sequence (an )n∈N and (bn )n∈N ...
Introduction
... 2 is a common factor to both 6 and 2. Both terms also contain an x. So we factorise by taking 2x outside a bracket. 6x2 – 2xy = 2x(3x – y) ...
... 2 is a common factor to both 6 and 2. Both terms also contain an x. So we factorise by taking 2x outside a bracket. 6x2 – 2xy = 2x(3x – y) ...
Number Fields
... • There are two special numbers called 0 and 1 so that: x+0 = x 1 · x = x. • Every number x has an opposite −x so that x + (−x) = 0. • Every number x, except 0, has an inverse x−1 so that x · (x−1 ) = 1. This list of rules, called the “Field Axioms,” allows us to decide what is and is not a field, a ...
... • There are two special numbers called 0 and 1 so that: x+0 = x 1 · x = x. • Every number x has an opposite −x so that x + (−x) = 0. • Every number x, except 0, has an inverse x−1 so that x · (x−1 ) = 1. This list of rules, called the “Field Axioms,” allows us to decide what is and is not a field, a ...
