Show that $8^{1/\pi}$ has infinitely many values. If it were possible to plot all its values, what would the picture look like.
How do I go about solving this.
Asked
Active
Viewed 171 times
8
-
2http://books.google.co.in/books?id=Ph49AAAAIAAJ&pg=PA238&lpg=PA238&dq=de+moivre's+theorem+for+irrational+index&source=bl&ots=D18uOAYTUN&sig=PfhZdBoavgHCfbVXzGCXQ6ckhnw&hl=en&sa=X&ei=mlNlUI6WA8_trQe7pID4Dw&ved=0CDoQ6AEwAw#v=onepage&q=de%20moivre's%20theorem%20for%20irrational%20index&f=false – lab bhattacharjee Sep 28 '12 at 07:38
1 Answers
2
Hint: $a^b = \exp(b \log a)$. The values of $\log a$ are $y + 2 \pi i n$ where $y$ is one value and $n$ is an arbitrary integer.
Robert Israel
- 448,999