Complex number

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Numbers with two dimensions are called complex numbers. You write these as

z = x₀ e₀ + x₁ e₁

and they consist of the real number x_a and the units

{ e₀ , e₁ }

In the multiplication of the units { e₀ , e₁} the sequence plays no role.

× e₀ e₁

e₀ e₀ e₁

e₁ e₁ −e₀

The unit e₀ is the real number 1. Complex numbers can be used to describe a rotation in two dimensions.

This notation was proposed in 1844 by the German mathematician Hermann Grassmann, who developed linear algebra.