Structured route

Geometry, Complex Numbers & Vectors

A practical route through points, lines, the Argand plane, vector products, and mechanics-style calculations. Start with the kind of problem in front of you, then move sideways when the method connects.

A sensible order through the tools

  1. Use distance, gradient, and line equations until the coordinate picture feels automatic.
  2. Switch to complex numbers when a point becomes a number with direction, modulus, and argument.
  3. Use vector products when the question asks for angle, projection, area, work, or moment.

Coordinate geometry

Coordinate geometry

Start here when a question is about points, lines, gradients, or shortest distances on a plane.

Complex numbers

Complex numbers

Use these when numbers move onto the Argand plane and arithmetic starts to behave like scaling plus rotation.

Vector algebra

Vector algebra

Move from coordinates to directed quantities: components, angles, products, areas, and perpendicular directions.

Engineering applications

Engineering applications

Apply the same algebra to circuits and mechanics, where the numbers carry units and physical meaning.

Roadmap

Planned next pages

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