# 1: Complex Numbers

- Page ID
- 9953

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- 1.3: Algebra of Complex Numbers
- The complex numbers form a mathematical “field” on which the usual operations of addition and multiplication are defined. Each of these operations has a simple geometric interpretation.

- 1.5: Representing Complex Numbers in Vector Space
- So far we have coded the complex number z=x+jy with the Cartesian pair (x,y) and with the polar pair (r∠θ) . We now show how the complex number z may be coded with a two-dimensional vector z and show how this new code may be used to gain insight about complex numbers.

- 1.6: An Electric Field Computation
- We have established that vectors may be used to code complex numbers. Conversely, complex numbers may be used to code or represent the orthogonal components of any two-dimensional vector. This makes them invaluable in electromagnetic field theory, where they are used to represent the components of electric and magnetic fields.