- Ch. 1Complex Numbers and Their AlgebraAdd one new number with i² = −1: complex numbers are points of the plane.
- Ch. 2Modulus and Argument (I)In polar form, multiplying means: moduli multiply, arguments add.
- Ch. 3Complex Numbers and Equations|z−a| is a distance: modulus equations are curves; non-real roots pair up.
- Ch. 4Adding and Subtracting VectorsVectors slide freely: chain them head to tail to add; a closed chain sums to 0.
- Ch. 5The Inner Producta·b is the length of a times the signed shadow of b on a.
- Ch. 6Vectors in SpaceWith coordinates, angles and distances in a solid become arithmetic.
- Ch. 7Roots of Unity and Their UsesRoots of unity form a regular n-gon and sum to 0, which filters coefficients.
- Ch. 8Modulus and Argument (II)Bound moduli with the triangle inequality; herd arguments into a half-plane.
- Ch. 9Applications of Complex Numbers and VectorsPoints as complex numbers: rotations are products, concyclic means a real ratio.