Complex numbers can be written as vectors. The addition and
subtraction properties of multiples of complex numbers are then
inherited from the addition and subtraction properties of multiples
of vectors.
We can write the complex number

as
the vector

and
the complex number

as
the vector

Then

It follows then that

This
is shown on the Argand diagram below.
In fact, the addition and subtraction of multiples of complex
numbers can also be considered an algebraic property.
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