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The 11 pages that link to Complex multiplication, each with the reason it gives.

• Complex numberBroader topic: Its rule turns multiplication into a combination of scaling and rotation.

• Complex planeRelated: Its geometric effect combines changes in distance from the origin and angle.

• Cauchy–Riemann equationsRelated: The equations express the requirement that a derivative act locally by complex multiplication.

• Class field theoryRelated: Complex multiplication constructs abelian extensions of imaginary quadratic fields.

• Imaginary unitRelated: Multiplying by i turns each complex number through a quarter-turn.

• Polar formRelated: In polar form, multiplying magnitudes and adding angles performs this operation.

• Hilbert class fieldRelated: For imaginary quadratic fields, singular moduli can generate the Hilbert class field.

• De Moivre's formulaRelated: Repeated multiplication explains why taking a power multiplies the argument.

• Imaginary numberRelated: It explains products such as i times i, which equal −1.

• Brahmagupta–Fibonacci identityRelated: The identity is the modulus-squared rule for multiplying complex numbers.

• Stark–Heegner theoremRelated: Stark’s proof uses complex multiplication to establish the decisive class-number-one classification.