Question

What is the absolute value of the complex number -4 - sqrt of 2i? i=sqrt of -1.

Answer 1

\(\large\color{black}{ \left| -4-\sqrt{2i} \right| }\)

Answer 2

Right?

Answer 3

Yes

Answer 4

Well, you know that for,
\(\large\color{black}{ \left| -a-b \right| =a+b }\)

( when \(\large\color{black}{ a >0 }\) and \(\large\color{black}{ b>0 }\) )

Answer 5

I myself though, haven't dealt with an absolute value of an imaginary number when I was in school.

Answer 6

Yes.

Answer 7

so, what will \(\large\color{black}{ \left| -4-\sqrt{2i} \right| }\) be?

Answer 8

It would be \[4+\sqrt{2i}\]

Answer 9

Yes:)

Answer 10

which would simplify into \[4+\sqrt{-1}\] The problem is, I don't know how to simplify it anymore and this is not apart of the possible answers I can give.

Answer 11

I don't see any way to simplify \(\large\color{black}{ 4+\sqrt{2i} }\).
And when you have an \(\large\color{black}{ i }\), you can just leave it as \(\large\color{black}{ i }\), without re-writing it as a \(\large\color{black}{ \sqrt{-1} }\).

Answer 12

wait, actually you can.

Answer 13

When you take 2i, you are pretty much just taking i*i, which is -1.

Answer 14

http://www.wolframalpha.com/input/?i=4%2B%E2%88%9A%282i%29

I do not know how he gets that though...

Answer 15

And what, here is the magic.
http://www.wolframalpha.com/input/?i=absolute+value+of+%7B-4-%E2%88%9A%282i%29%7D

I was wrong.

Answer 16

Mean either. I had to guess on my assignment, 'cause it was timed and i had 30s left. I got it wrong, but I'll still try to figure it out later. I have to go eat supper now.

Answer 17

okay.... good luck.