Complex powers

Level pending

$i^{\frac{1}{i}}$ Equals

1 solution

Pratik Shastri
Feb 11, 2014

Let $y=i^\frac{1}{i}$

$\ln y=\frac{1}{i}\times \ln i$

$i=e^{i\times \frac{\pi}{2}}$

So , $\ln y=\frac{1}{i}\times\frac{i \times \pi}{2}\times \ln e$

$y=e^{\frac{\pi}{2}}=\boxed{4.81}$

let i^{1/i}=y

  i=y^{i}
  i^{4}=y^{4i}
  1=y^{4i}
   1^{1/4i}=y 
    y=1 (anything raise to power one is one itself ) 
         what about this one?????????????

Anurag Shekhar - 7 years ago

This is like saying...

$y^2-5y+6=0$

$\rightarrow y=2,y=3$

$\rightarrow 2=3$

Pratik Shastri - 6 years, 12 months ago

No, that's a different analogy. The problem is that one raise to any power is not always one. Not if the power is complex.

Kenny Lau - 6 years, 11 months ago

@Kenny Lau – @Kenny Lau 1 raised to any power is 1. (The principal root is always 1).

Anyways, here it is $\textbf{only 1}$ .

Pratik Shastri - 6 years, 10 months ago