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.
