Question

How would you simplify
(3+i)(4+2i)?​

Answer 1

11 + 10i

Explanation:

Note that we're multiplying two binomials here, and thus may use the FOIL method. This requires four multiplications, as follows:

3*4 + 3*2i + 4i - 1 (The last term is 1 because i(i) = i^2 = -1.)

Simplifying, we get:

12 + 6i + 4i -1, or:

11 + 10i

Answer 2

(3 + i)(4 + 2i) = 10 + 10i

Explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

`(3+i)(4+2i)\\\\=(3)(4)+(3)(2i)+(i)(4)+(i)(2i)\\\\=12+6i+4i+2i^2\qquad\text{combine like terms}\\\\=(12-2)+(6i+4i)\\\\=10+10i`