Question

Find the value of:

$i^i$

• A. $0$
• B. $e^{-(4n+1)\frac{\pi }{2}}$
• C. $e^{(4n+1)\frac{1}{2}}$
• D. $1^{-(4n+1)\frac{\pi }{2}}$

Answer 1

Answer: (B)

$e^{-(4n+1)\frac{\pi }{2}}$

$i$ can be expressed as$e^{\left(i\pi /2\right)}$

So, $i^i$ can be expressed as $(e^{\left(i\pi /2\right)}{)}^i$

Hence, $i^i=e^{\left[i^{\left(2\right)}\frac{\pi }{2}\right]}$

we know that $i²=-1$

$⟹i^i=e^{(-\pi /2)}$

So in general, $i^i=e^{-(2n\pi +\pi /2)}=e^{-(4n+1)\frac{\pi }{2}}$