How do you multiply a number containing a complex number?

Answer 1

One way, use binomial multiplication. Example: (w + x)*(y + z) = {using the FOIL method} w*y + w*z + x*y + x*z, so if we have two complex numbers multiplied:

(a + b*i)*(c + d*i) = a*c + a*d*i + b*c*i + b*d*i*i, but i*i = -1, so this becomes:

(a*c - b*d) + (a*d + b*c)*i

Another way to express complex numbers is as a magnitude and an angle. If this is the case, then you multiply the two magnitudes, and add the angles, then reduce the resultant angle to within -180° and +180°.

If you have a real X complex, then just use {b=0} in (a + b*i), so then you have:

(a*c) + (a*d)*i *Or if using the polar coordinates, take the angle as 0° for a positive real number and 180° for a negative real number, then add the angles.