Which of the following is not one of the 8th roots of unity?

i
1 + i
+ i

Question

Which of the following is not one of the 8th roots of unity?

i
1 + i
 + i

tkhunny · Answer

Unity is 1.
It must have a magnitude of 1, so that |1|^8 = 1 -- This eliminates the middle one.
What say you of the other two?

tkhunny · Answer

???  And, what;s the difference betweel "i" and "+i"?  Is the second just a typo?

anonymous · Answer

no it was sqrt2/2 +sqrt2/2

tkhunny · Answer

Well, anything with a magnitude that is not ONE cannot be a root of Unity.

Check out the magnitudes.

i has a magnitude of 1
-1 has a magnitude of 1

1+i has a magnitude of sqrt(2) -- Too big!

anonymous · Answer

so is it just i?

tkhunny · Answer

No, read the question again.  I missed it the first time.  It wants to know which are NOT 8th roots of Unity.  You must find ALL of them with a magnitude that is not 1.

perl · Answer

$$
\Large {z^8 =1  \~\	herefore \~\
\ z =   1, -1, i, -i,\
 \frac12\sqrt2+(1/2i)\sqrt2, \-(1/2)\sqrt2-1/2i\sqrt2,\
 (1/2)\sqrt2-(1/2i)\sqrt2, \-(1/2)\sqrt2+(1/2i)\sqrt2
 
}
$$

mathmath333 · Answer

what r ur options @mudwagaman9