Summary Notes & Proofs for Test 5 (MAM1000W) - \$3.37   Add to cart

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# Summary Notes & Proofs for Test 5 (MAM1000W)

Summarised Notes & Proofs made according to the scope given to us for Test 5 in 2019. Topics: • Factorials - Resource book 2 • 1-1 functions and permutations - Resource book 2 • Falling factorials - Resource book 2 • Combinations - Resource book 2 • Binomial coefficients and Pascal’s Triangle - Resource book 2 • The Binomial Theorem - Resource book 2 • Maclaurin and Taylor polynomials - Stewart 11.10 (polynomials, and not series). • Elementary properties of complex numbers (all complex numbers sections are taken from the resource book). • Modulus, the complex plane, and Argand Diagrams • The complex conjugate and division of complex numbers • Multiplication and De Moivre’s Theorem • Argument and modulus-argument form • The complex exponential function • The complex trigonometric functions • n^th roots • Roots of polynomials And the proofs that you are expected to know (potentially among others): • Pascal's identity • Be able to prove the properties of various aspects of complex numbers (modulus, complex conjugate, etc.). • De Moivre’s Theorem (Note that you can’t use the complex exponential function in your proof!) • The non-real roots of a polynomial with real coefficients occur in complex conjugate pairs • Every polynomial with real coefficients can be written as a product of real linear and irreducible quadratic factors

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