1.2 Number and algebra - AHL content

• Use logarithm laws for products, quotients and powers.

• In examinations, logarithm bases are 10 or e.

• Simplify numerical and algebraic expressions with rational exponents.

• Include negative and fractional powers.

• Find sums of infinite geometric sequences.

• Connect convergence to limits, fractals and Markov chains.

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

• Calculate sums, differences, products, quotients and powers of complex numbers.

• Use Argand diagrams and complex roots of real-coefficient quadratics with negative discriminant.

• 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 exponential forms.

• Use products, quotients and integer powers; roots are not required.

• Interpret complex operations geometrically and model sinusoidal phase shifts.

• Use matrix terminology, order, equality, addition, subtraction, scalar multiplication and multiplication.

• Know identity/zero matrices, determinants and inverses; hand calculation is limited to 2x2 inverses/determinants.

• Write systems as Ax=b and solve with inverse matrices; apply matrices to coding, decoding and systems.

• Find eigenvalues/eigenvectors and characteristic polynomial for 2x2 matrices.

• Diagonalize 2x2 matrices with distinct real eigenvalues.

• Use M^n=PD^nP^-1 for powers and applications such as population movement or predator-prey models.