Complex number help? Watch

hannnahx
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#1
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've been asked to calculate what the following is:

(i)(i^2)(i^3)(i^4)..........(i^2 014) = ??

i know the individual values for the separate parts but unsure what the answer would be all together, a quick way to do this would be much appreciated
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BabyMaths
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(Original post by hannnahx)
've been asked to calculate what the following is:

(i)(i^2)(i^3)(i^4)..........(i^2 014) = ??

i know the individual values for the separate parts but unsure what the answer would be all together, a quick way to do this would be much appreciated
What's that last bit supposed to be. Assuming it's just a typo, add the powers and then simplify.

Edit: Oh, is it i^{2014}?

Still, just add the powers and then simplify.
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hannnahx
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Yeah typo sorry, thank you
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Hasufel
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whatever number you get for the power, one way you could do it is you can then split it up again into "i`s" to read:

(i^{a})^{1000000} \times( i^{b})^{10000} \times (i^{c})^{1000} \times(i^{d})^{100} \times((i^{e})^{5})^{5} \times i^{5}

(a,b,c,d,and e are all small simple integers - well, you have to do slighly more for c - , so its easy)
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'Ello Dave!
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(Original post by hannnahx)
've been asked to calculate what the following is:

(i)(i^2)(i^3)(i^4)..........(i^2 014) = ??

i know the individual values for the separate parts but unsure what the answer would be all together, a quick way to do this would be much appreciated
Use the sum of a series to find the sum from 1 to 1024.
Also use the fact that (i^n) cycles through 4 different values every time you multiply.
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