Question

@mathstudent55

Answer 1

It's number 2 I'm entirely lost.

Answer 2

\(\sqrt{-48} \)

The first thing, is express -48 as -1 * 48.
Then you know that sqrt(-1) = i

\(\sqrt{-48} = \sqrt{-1 \times 48} = i \sqrt{48}\)

Ok so far?

Answer 3

\(\sqrt{-48} = \sqrt{-1 \times 48} = \sqrt{-1} \times \sqrt{48} =i \sqrt{48}\)

Answer 4

The third option

Answer 5

So anytime it's a negative square root I'm gonna multiply -1 into it?

Answer 6

Now we simplify sqrt(48)

Answer 7

\(i\sqrt{48} = i \sqrt{16 \times 3} = i\sqrt {16} \times \sqrt{3} = 4i\sqrt{3}\)

Answer 8

[4i \sqrt{-48}\]

Answer 9

Anytime you take the square root of a negative number, you need to take out a square root of -1, which is i.

Answer 10

You are correct.

Answer 11

Oohh okay that makes sense. cx I get it now :) Thanks

Answer 12

Do you need to do problem 3?

Answer 13

For number three I got 1. It want's me to simplify \[i ^{38}\]

Answer 14

How did you get 1?

Answer 15

i^(4n) = 1

.__. am I wrong..

Answer 16

Your formula is correct, but 38 is not divisible by 4, so 38 is not 4n.

Answer 17

We have by definition that \(\sqrt{-1} = i\)
Then we can conclude that \(i^2 = -1\)
We also know by definition that \(a^0 = 1\) for any a with the possible exception of a = 0.

Answer 18

oh wait okay
\[i ^{(2n)}\]= -1

Answer 19

Now we start with exponent 0:
\(i^0 = 1\) since a^0 = 1
\(i^1 = i\) since for every a, \(a^1 = a\)
\(i^2 = -1\)
\(i^3 = i^2 \times i = -1 \times i = -i\)
\(i^4 = i^3 \times i = -i \times i = -(-1) = 1\)
Now you see that for exponent 4 we have teh same as for exponent 0.
The pattern continues and repeats.

Answer 20

38 is 2 more that 36.
36 is a multiple of 4.
We need the exponent that corresponds to 2 more than a multiple of 4.

\(i^{38} = i^{36 + 2} = i^2 = -1\)

Answer 21

That's how I do it.

Answer 22

Im confused now .-.
was I right in the first place with the answer of 1
or is the answer now -1?

Answer 23

Answer is -1, not 1.

Answer 24

Oh okay I just looked over what you just put
\[i ^{38}=i ^{36+2}=i ^{2}=−1\]
that makes sense I get it I was looking at what you said before that.

Answer 25

At every multiple of 4 exponent, i^n = 1.

The pattern is:

1 (exponent is multiple of 4)
i (exponent is multiple of 4) + 1
-1 (exponent is multiple of 4) + 2
-i (exponent is multiple of 4) + 3

Answer 26

Great.

Answer 27

:) Thank you!

Answer 28

I have 5 min left.
Then I have to go.
Do you have 1 more problem we can try to do quickly?

Answer 29

You're welcome.

Answer 30

I just need you to make sure I have these two right these are the easy ones :)

Answer 31

4 & 5 both are correct

Answer 32

Thank you! You are absolutely amazing :) I gave you a testimonial and if I could give you more medals I would! :)

Answer 33

That's funny, because without knowing you did for me, I gave you a testimonial too.

Answer 34

You're welcome.
Thanks for your kind words.
If you find me online again and have questions, feel free to ask.

Answer 35

Okay :) and thank you!

Answer 36

I found a way to give you more medals cx haha