Question

find general value of i^i??

Answer 1

. Hi friend!!

i can be expressed as e^(iπ/2)

So, i^i can be expressed as (e^(iπ/2))^i

=e^(i²π/2)

we know that i²=-1

=e^(-π/2)

I hope this will help u ;)

Answer 2

Thus, $i^{i}$ value is $e^{-\frac{\pi}{2} }$

Step-by-step explanation:

Given,

Find general value of $i^{i}$ ?

We also know,

  $i=e^{i\frac{\pi}{2} }$

⇒$i^{i}=(e^{i\frac{\pi}{2} })^{i}$

⇒$i^{i}=e^{i^{2} \frac{\pi}{2} }$

where $i^{2}$ value is $-1$

⇒ $i^{i}=e^{-\frac{\pi}{2} }$

∴ $i^{i}$ value is $e^{-\frac{\pi}{2} }$