Question

What is 4x + 3i * 7x +4i

Answer 1

If you're multiplying these terms with imaginary parts, do it just like you would any binomial multiplication.  (4x+3i)(7x+4i).  FOIL-ing that out we get, before simplification, $28 x^{2} +16ix+10ix+12 i^{2}$.  There are 2 things to simplify here:  Combining like terms and then dealing with the squared i.  $i^{2}$ is equal to -1, so 12(-1) = -12.  Then we will combine the ix terms and in the end we will have $28 x^{2} +26ix-12$