Question

Find the product of the complex number and its conjugate.
1 + 3i

Answer 1

Do they mean (1 + 3i)^2?

Answer 2

that equals to 4

Answer 3

The conjugate of 1 + 3i is 1 - 3i
(1 + 3i)(1 - 3i) = (1)^2 + 3i - 3i - (3i)^2
The two middle terms drop out, and you are left with (1)^2 - (3i)^2
1^2 = 1
3^2 = 9
i^2 = (√-1)^2 = -1
You end up with 1 - {(-1)(9)}
So it becomes 1 - (-9)
Which is 1 + 9
which equals 10

Answer 4

If you are given complex number \(a+bi\), then its conjugate would be \(a-bi\)

So you have \((1 + 3i)(1 - 3i)\)

Answer 5

Oh, ok. Just my lack of vocabulary.

Answer 6

ya it is 10

Answer 7

@jazminjones1252 you are wrong

Answer 8

wait 1 plus 3 equals to 4i and that is the answer

Answer 9

\((1 + 3i)(1 - 3i)\\~\\1^2 - (3i)^2\\~\\1 - (-9)\\~\\1+9\\~\\\boxed{10}\)

Answer 10

@jazminjones1252

Answer 11

ok