eeblue
why is i3 equals to -i??
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eeblue
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eeblue
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isnt it?? :'(
03453660
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no
phi
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i^3 = i*i*i
what is (i*i) ?
03453660
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03453660
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eeblue
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omg!! I am so dumb..
03453660
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you are learning thats great
eeblue
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ohh!! I think I am starting to get it.. then could you try solving i120 to let me see?
03453660
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is this i^120???
phi
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I would first figure out what is i^4= i*i*i*i
eeblue
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what about large numbers to simplify? I cant be doing square rootss of -1 all the time right?
eeblue
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i^120?? i^99 for example..
phi
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what is i^4 ?
eeblue
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1?
03453660
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its very easy
all you do is you have to remember some formulas
i^2 = -1 , i^3 = -1 , and i^4 = 1
phi
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yes
now if you wrote out i^120 it would be
(i*i*i*i) * (i*i*i*i) * .... * (i*i*i*i)
phi
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how many groups of 4 i's are there?
03453660
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i^120 = (i^2)^60 = (-1)^60 = 1
eeblue
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how many groups of 4 i's? 30?
phi
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and 1 times itself 30 times is still 1
03453660
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no dont go for grouping method
eeblue
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omg!! confused!! :'(( why there's maths on earth!! urgh!!
eeblue
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eeblue
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why plus 0?? *got it from a website*
phi
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The first step to understanding this is to understand that you have
1*1*1*1*...*1 (30 times)
if the problem were i^121
(one more i), it would be
1*1..*1 * i one i left over
03453660
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eeblue
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okay.. then??
phi
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once you get the idea, you can use the idea of exponents
\[ i^{ab} = (i^a)^{b} \]
eeblue
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ohh!! okay!! I think I am starting to understand.. omg!!
eeblue
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03453660, could you try solving i^99?? I would like to see..
eeblue
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eeblue
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lost :((
amistre64
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what is the remainder when you divide 99 by 4?