Complex Number Problem #1

I’ve come across many questions from students regarding complex numbers, and here is one thats quite fun to deal with!

\sqrt{-1}^{\sqrt{-1}}

Now this is really interesting, but can be solved with a bit of manipulation. We all know this is akin to i^i

We know that \sqrt{-1}=e^{i\frac{\pi}{2}}

\sqrt{-1}^{\sqrt{-1}}

= e^{i\frac{\pi}{2}\sqrt{-1}}

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

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

= e^{-\frac{\pi}{2}}

Now our end result is a real number!

Like mentioned with regards to Euler’s Identity, it is really very amazing how complex numbers actually work!

Comments
    pingbacks / trackbacks

    Leave a Comment

    4 × four =

    Contact Us

    CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

    Not readable? Change text. captcha txt

    Start typing and press Enter to search