Question

Does i^2=sq root of -1?

Answer 1

i^2 = -1

Answer 2

OK?

Answer 3

does ok mean yes

Answer 4

OK means "Do you understand, get it, agree etc"

ie i^2 = -1 (i^2 does NOT = sq rt of -1)

Answer 5

no- I don't get it

Answer 6

Why not?

Answer 7

isn't sq. rt of anything always a positive number

Answer 8

how do you get the square root of a negative number?

Answer 9

sq rt of -25 is 5 or not

Answer 10

How can it be? 5*5 = 25 and -5*-5 is also 25

Answer 11

so what is sq rt of -25

Answer 12

You know the rule sqrt (ab) = sqrt (a) sqrt(b) ?

Answer 13

yes

Answer 14

Right, so we have sqrt(-25) = sqrt(25)sqrt(-1) Agree?

Answer 15

yes

Answer 16

Now we have i^2 = -1 and so we can think of i = sqrt(-1)

Answer 17

ok I^2 =1 not -1 thank you

Answer 18

So sqrt of -25 = 5i

Answer 19

i^2 = -1

Answer 20

5i*5i = 25i^2 = 25*-1 = -25

Answer 21

so now I am lost again I thought i^2=1 but no it =-1

Answer 22

I keep telling u i^2 = -1 (it's a definition not something you have to prove)

Answer 23

ok I was missing that. I thought it wa equal to 1

Answer 24

U see how it works now?

Answer 25

Strictly speaking, if i^2 = -1 then there should be 2 roots i and -i but by convention we pick i as the principal one (similar to positive sq rt convention)

Answer 26

yes, and I am looking in my book at the -sq.rt. and what you are saying makes sense now. Thanks for the lesson

Answer 27

ur welcome