... (a + bi)(c + di) = ac + adi + bci + bdi2 = (ac − bd) + (ad + bc)i.
For any number z = a + bi we say the real part of z is
Re(z) = a,
and the imaginary part of z is
Im(z) = b.
Writing the complex numbers as 2-tuples instead, e.g., (a, b), they natually look like points,
or vectors on the xy-plane, wh ...