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
- Use distance, gradient, and line equations until the coordinate picture feels automatic.
- Switch to complex numbers when a point becomes a number with direction, modulus, and argument.
- 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
polar coordinate converter
polar curve plotter
parametric curve plotter
cycloid visualiser
complex roots visualiser
plane equation point normal
point to plane distance
scalar triple product calculator
coplanar vectors checker
vector triple product calculator
gauss jordan elimination solver
matrix multiplication calculator
inverse matrix calculator
bisection method calculator
newton raphson calculator
synthetic division calculator
polynomial method chooser