Education and Didactics

    

On the Decomposition of a Vector Using Complex Numbers

Authors: Aloys J. Sipers, Joh. J. Sauren

In this letter a theorem is stated on the decomposition of a vector with respect to two axes using complex numbers. This theorem may serve to develop exercises for education in mathematics and physics. In most physics exercises the vectors are given by their polar coordinates. Motivated by practical applications, we denote the vectors by their Cartesian coordinates. Cartesian coordinates provide a didactic aid to develop exercises which can be solved without the use of a calculator. The educational potential of the theorem is demonstrated by a numerical example.

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[v1] 2025-07-04 14:51:15

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