Template:Sequence of the Day for November 1

Intended for: November 1, 2012

Timetable

• First draft entered by Alonso del Arte on October 27, 2011 ✓
• Draft reviewed by Daniel Forgues on October 31, 2012 ✓
• Draft to be approved by October 1, 2012

Yesterday's SOTD * Tomorrow's SOTD

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A042972: Decimal expansion of

i √  i = i 1 / i = i  − i = (i  i  )  − 1 = 1 i  i

.

4.81047738096535165547...

Since

i  i  =  {e i π  / 2}  i  =  e  −  π  / 2,

this works out to

e  π  / 2

which is a real number! We all know about the square root of 2, and perhaps some of us have given some thought to the cubic root of 3, the fourth root of 4, the fifth root of 5, etc. Now, here’s the

i

th root of the imaginary unit

i = 2√   − 1

!
By now, you probably want to find out the

e

th root of

e

or the

π

th root of

π

... or are you looking for the

ϕ

th root of

ϕ

or the

2√  2

th root of

2√  2

?