Question

(1 + 3i)(3 + i): what is the answer to this

Answer 1

Use FOIL.
Then combine like terms.
Remember that \(i^2 = -1\)

Answer 2

Start with FOIL and show all 4 products.

Answer 3

I tried but Idk how to get the answer @mathstudent55

Answer 4

Can you tell me the answer then explain how to do it

Answer 5

Have you learned how to multiply binomials using FOIL?
FOIL stands for (F)irst, (O)utside, (I)nside, (L)ast and it shows you the order of multiplying the terms of two binomials.
I'll show you how it works with these two binomials: (x + 3)(x - 5)
First: multiply the two first terms together: x * x = x^2
Outside: multiply the outside terms together: x * (-5) = -5x
Inside: multiply the inside terms together: 3 * 5x = 3x
Last: multiply the last terms together: 3 * (-5) = -15
Now write all the products in one line and combine like terms:
(x + 3)(x - 5)
= x^2 - 5x + 3x - 15
= x^2 - 2x - 15

Answer 6

Now we can do the same with your problem.
\((1 + 3i)(3 + i)\)

F O I L
\(= 1 * 3 + 1 * i + 3i * 3 + 3i * i\)

\(= 3 + i + 9i + 3i^2\)

\(= 3 + 10i + 3 * (-1)\)

\(= 3 + 10i - 3\)

\(= 10i\)