When dealing with complex numbers, simply pretend that the real part is a real animal, such as a beetle, and that the imaginary part is an imaginary animal, such as a 'giraffe'.
Beetle                                                                 'Giraffe'

When adding, simply add beetles to beetles and 'giraffes' to 'giraffes'.

When multiplying, simply remember that men beetles and lady beetles mate to produce baby beetles, and that men 'giraffes' and lady 'giraffes' mate to produce baby beetles, as shown below.
=
X
Easy!
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