What is i^(Googol)?
Date: 05/27/2000 at 10:06:43 From: Grant Feest Subject: Googol What is the value of i raised to the googol power, where i is the square root of -1? Thank you
Date: 05/29/2000 at 15:06:48 From: Doctor TWE Subject: Re: Googol Hi Grant - thanks for writing to Dr. Math. Let's see, i^0 = 1 any x^0 = 1, except x = 0 i^1 = i any x^1 = x i^2 = -1 by def; [sqrt(-1)]^2 = -1 i^3 = i^2*i = (-1)*i = -i i^4 = i^2*i^2 = (-1)*(-1) = 1 i^5 = i^4*i = (1)i = i i^6 = i^4*i^2 = (1)*(-1) = -1 i^7 = i^6*i = (-1)*i = -i i^8 = i^6*i^2 = (-1)*-1 = 1 Do you see a pattern developing here? Now a googol is 10^100 (a one followed by 100 zeros.) Based on the above pattern, can you find a shortcut to finding i^(googol)? I hope this helps. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
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