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### What is i^(Googol)?

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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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Associated Topics:
High School Exponents
High School Imaginary/Complex Numbers

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