Complex Numbers — H2 Math prelim questions & worked solutions
Anglo-Chinese Junior College · Paper 1Quartic conjugate roots plus modulus-argument and cosine rule on an Argand diagram.Anderson Serangoon Junior College · Paper 2Modulus-argument form, Argand-diagram geometry, and an exact value for tan(11π/24) via a rhombus.Catholic Junior College · Paper 2Conjugate roots, factorising a real quartic, and trapezium area on an Argand diagram.Dunman High School (DHS) · Paper 1Parametric complex locus to ellipse, argument of a sum, and a quadratic from non-conjugate roots.Eunoia Junior College · Paper 1Complex square root, cubic roots and a substitution mapping one equation to another.Hwa Chong Institution · Paper 1Quartic roots via conjugate pairs and even symmetry, plus reciprocal-root substitution.Jurong Pioneer Junior College · Paper 2Real-coefficient cubic roots, conjugate pairs, and showing an Argand parallelogram is a square.National Junior College · Paper 1Solve simultaneous complex equations, then interpret w/z = i as a 90° rotation.National Junior College · Paper 2Find modulus and argument of a complex number, then use Argand-diagram geometry to deduce arg(2-w).Nanyang Junior College · Paper 1Argand geometry: rhombus from equal moduli, arg of sum, and reflecting a point in OP.Nanyang Junior College · Paper 2Conjugate-pair roots of an imaginary-coefficient cubic, then x to -x substitution for the related cubic.Raffles Institution · Paper 1Complex number argument under scaling and rotation, plus triangle geometry of f(z)=z^2-2z.River Valley High School · Paper 1Use the conjugate root theorem to find cubic coefficients b, c, d in terms of a.River Valley High School · Paper 1Solve a quadratic with complex coefficients via a complex square root.River Valley High School · Paper 2Rotate a complex vector 90° and use parallelogram diagonals to find vertices.St Andrew's Junior College · Paper 1Simultaneous complex equations with a modulus, plus a conjugate-point Argand argument.St Andrew's Junior College · Paper 2Root symmetry, conjugate roots, and factorising a complex-coefficient cubic.Temasek Junior College · Paper 1Solve simultaneous complex equations with modulus, then find square vertices on an Argand diagram.Tampines Meridian Junior College · Paper 1Conjugate roots of a real cubic, Argand geometry, and proving tan(3π/8)=1+√2.Victoria Junior College · Paper 1Solve a modulus equation, find cube roots, and locate the circle through them.Victoria Junior College · Paper 2Argand diagram geometry from multiplication-as-rotation, Cartesian form, and an exact tan value.