What you’ll learn7 learning objectivesChoose one objective for a focused lesson, or study the complete topic.—AHL 1.9 (HL)—Logarithm laws• Use logarithm laws for products, quotients and powers.• In examinations, logarithm bases are 10 or e.Syllabus objective—AHL 1.10 (HL)—Rational exponents• Simplify numerical and algebraic expressions with rational exponents.• Include negative and fractional powers.Syllabus objective—AHL 1.11 (HL)—Infinite geometric sequences• Find sums of infinite geometric sequences.• Connect convergence to limits, fractals and Markov chains.Syllabus objective—AHL 1.12 (HL)—Complex numbers• 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.Syllabus objective—AHL 1.13 (HL)—Complex forms and applications• 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.Syllabus objective—AHL 1.14 (HL)—Matrices• 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.Syllabus objective—AHL 1.15 (HL)—Eigenvalues and eigenvectors• 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.Syllabus objective