What is the purpose of <-i> in a complex number subgroup?

[foreverdream]

Well I generally haven an idea about subgroup of a group and generators. But I fail to understand following:
({1,-1,i,-i},X)
I can see
<1>={1}
<-1>={-1,1}
<i>={i,-1,-i,1}
But simply have no idea about <-i>
How can you work with -i?

 

[mathman]

You would get more responses if you could explain your terminology. < >, { , , , }, etc.

 

[micromass]

Calculate $-i$, $(-i)^2$, $(-i)^3$, and so on...

 

[foreverdream]

Yes but that's what I don't know how to because -i is imagery number that's is - sq rt of 1? Isn't it ?

 

[micromass]

Yes but that's what I don't know how to because -i is imagery number that's is - sq rt of 1? Isn't it ?

The multiplication rule for complex numbers is clear:

$$(a+bi)(c+di)=(ac-bd)+(bc+ad)i$$

by definition.

 

[foreverdream]

Ok i will try and see if I nail this. Will get back to you thanks foe guiding

 

[foreverdream]

Not much luck. Basically I need to work out subgroups generated by this group and I am going all mad in sign area

 

[Deveno]

Not much luck. Basically I need to work out subgroups generated by this group and I am going all mad in sign area

you already know that -i = i³, right?

and you already know that i⁴ = 1 as well, correct?

so (-i)² = (i³)² = i⁶ = (i⁴)(i²) = i² = -1.

now try to deduce what (-i)³ and (-i)⁴ should be.

 

[foreverdream]

Oh I worked it out thanks. But I have another question. I would like to attached a typed word doc it's easy then typing all Maths. Do you have e mail I can talk to you directly ? If u don't mind.

 

[Deveno]

Oh I worked it out thanks. But I have another question. I would like to attached a typed word doc it's easy then typing all Maths. Do you have e mail I can talk to you directly ? If u don't mind.

my policy (i can't speak for other forum members), is to respond to the first private message in order to request that people ask their questions on the forum. if someone persists, i block them.

i don't mean to be harsh, but that's the way i do things. if you want to post an image file, there are ways to do that on these forums (use the "Advanced" tab when posting, and be sure to preview your post to make sure you have done so correctly).

"math typing" is handled on these forums through Latex. there is a stickied guide to Latex HERE:

https://www.physicsforums.com/showthread.php?t=546968

 

[micromass]

my policy (i can't speak for other forum members), is to respond to the first private message in order to request that people ask their questions on the forum. if someone persists, i block them.

It's ok to report people who bother you. The behaviour is unacceptable.

To the OP: you can attach the word document in a post if you want.

 

[foreverdream]

I am fairly new so I didn't mean to bother anyone. If that's how this comes across apologies. I have not used latex so thought sending file will be quicker. That's all.