why are there 4 answers to the imaginary number i? The 4 answers are -1, -i, 1, and j. Can someone help me ? this is 10th grade math

Question

irishboy123 · Answer

maybe you are looking at the 4 fourth roots.

wintersuntime · Answer

okay thank you

anonymous · Answer

i think you are looking at $i$ to various powers

anonymous · Answer

not the fourth roots, which is completely different

anonymous · Answer

$$i^1=i\
i^2=-1\
i^3=-i\
i^4=1$$

wintersuntime · Answer

oh okay thank you that makes more sense

fibonaccichick666 · Answer

I will also add, that i is just a defined variable.  i always is equal to the square root of negative 1.  That is its definition.  

Then I agree with sat, I think that is what you were actually looking at

wintersuntime · Answer

thank you but why are the various powers to i equal 4 same answers

anonymous · Answer

$$i^2=-1$$ is the definition of $i$
the number whose square is $-1$
i.e $i=\sqrt{-1}$

anonymous · Answer

so $i^3=-1\times i=-i$

fibonaccichick666 · Answer

ah, so i like I said, is the square root of -1,  now.  If you take $$\sqrt{-1}*\sqrt{-1}=(\sqrt{-1})^2=-1$$

anonymous · Answer

and $i^4=-i\times i=-(-1)=1$

fibonaccichick666 · Answer

then sats, for cube and fourth

anonymous · Answer

once you get to $i^4=1$ it should be pretty clear that you start over

wintersuntime · Answer

oh alright thank you guys

anonymous · Answer

$$i^4=1\
i^5=1\times i=i\
i^6=i\times i=-1\
etc$$

anonymous · Answer

$$i^{2003}=i^3=-i$$

fibonaccichick666 · Answer

np