Question

The product of (3+2i) and a complex number is (17+7i)

Answer 1

`\large\boxed{(3+2i)(17+7i)=37+55i}`

Explanation:

`\text{Use}\ \bold{FOIL}\ (a+b)(c+d)=ac+ad+bc+bd,\ \text{and}\ i^2=-1:\\\\(3+2i)(17+7i)\\\\=(3)(17)+(3)(7i)+(2i)(17)+(2i)(7i)\\\\=51+21i+34i+14i^2\\\\=51+21i+34i+14(-1)\\\\=51+21i+34i-14\qquad\text{combine like terms}\\\\=(51-14)+(21i+34i)\\\\=37+55i`