How do you multiply (4 + 2i)(3 - i) ?

Jun 19, 2018

$14 + 2 i$

Explanation:

Like the way we would with real numbers, we can multiply out these binomials using the mnemonic FOIL (Firsts, Outsides, Insides, Lasts). This is the order we multiply in. We get

• First terms: $4 \cdot 3 = 12$
• Outside terms: $4 \cdot - i = - 4 i$
• Inside terms: $2 i \cdot 3 = 6 i$
• Last terms: $2 i \cdot - i = - 2 {i}^{2}$

Which simplifies to

$- 2 {i}^{2} + 2 i + 12$

Note that ${i}^{2} = - 1$, so we can plug this in for ${i}^{2}$. We'll get

$14 + 2 i$

Hope this helps!