Complex numbers
Chapter 30 of 10 strong
RESTS ONConvert exact complex components and use a stated principal argument conventionFOUNDATIONSApply exact compound and double-angle identities with valid domainsFOUNDATIONSCalculate finite arithmetic and geometric sums with explicit index boundsFOUNDATIONSConstruct induction proofs with a verified base, arbitrary-index hypothesis and justified next caseCH 1Interpret and calculate complex conjugates and exact modulusFOUNDATIONSConstruct direct, contrapositive and contradiction arguments with justified stepsCH 1Solve negative-discriminant real-coefficient quadratics over CFOUNDATIONSDivide one polynomial by a lower-degree polynomial, maintaining descending-power columns and zero placeholders, to obtain an exact quotient and a remainder of lower degreeFOUNDATIONS
De Moivre, complex roots and Argand regions
Polynomial factorisation over the complex field