1.2 Number and algebra - AHL content

• Use counting principles, permutations and combinations.

• Extend binomial expansion to fractional and negative indices.

• Exclude identical-object permutations, circular arrangements and proof of the theorem.

• Decompose rational expressions into partial fractions.

• Denominators have at most two distinct linear terms; numerator degree is lower than denominator degree.

• Use i where i^2 = -1 and Cartesian form z=a+bi.

• Know real/imaginary parts, conjugate, modulus, argument and the Argand diagram.

• Use polar form z=r(cos theta + i sin theta)=r cis theta and Euler form z=re^(i theta).

• Convert between Cartesian, polar and Euler forms; interpret sums, products and quotients geometrically.

• Know complex conjugate roots of real-coefficient polynomial equations.

• Use De Moivre's theorem for powers and roots of complex numbers.

• Include induction proof for positive integer powers; be aware of rational exponent extension.

• Use proof by mathematical induction and proof by contradiction.

• Use counterexamples to disprove statements, with explanation of why the counterexample works.

• Solve up to three linear equations in three unknowns algebraically and with technology.

• Identify unique, infinite or no solutions; find general solutions where appropriate.