To find only units of the Guassian ring are 1,-1, i and-i We can do as follows Take a +i b belongs to Z[i ] If possible c+ i d is the inverse of a+i b Then we get ac- bd = 1 and ad+ bc =0 Squaring adding we get (a^2 +b^2) (c^2+d^2) =1 which gives a^2+b^2 =1 Which gives the four cases 1,-1, i and -i Ok
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To find only units of the Guassian ring are 1,-1, i and-i
We can do as follows
Take a +i b belongs to Z[i ]
If possible c+ i d is the inverse of a+i b
Then we get ac- bd = 1 and ad+ bc =0
Squaring adding we get
(a^2 +b^2) (c^2+d^2) =1 which gives a^2+b^2 =1
Which gives the four cases 1,-1, i and -i
Ok
That's a really simple method, i too thought of that!!, I don't know why he went with such computation.
You didn't check 2 bar. 1 bar for Z/3Z
Notes mil sakte hai kya iske pdf?
Sir you tell " Non zero coefficient s are"!