# Math: two exponent questions
**URL:** https://boards.straightdope.com/t/math-two-exponent-questions/40358
**Category:** Factual Questions
**Created:** [November 8, 2000, 8:18pm UTC](https://boards.straightdope.com/t/math-two-exponent-questions/40358 "2000-11-08T20:18:12Z")
**Posts on this page:** 4
**Page:** 2
### Author:  [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)
#### Post date: [November 10, 2000, 6:48pm UTC](https://boards.straightdope.com/t/math-two-exponent-questions/40358/21 "2000-11-10T18:48:34Z")
> [@](#):
>
> I just want to know where your answer came from since you didn’t show your work.
That’s because I cheated. I plugged j^j into matlab, and backed out the e^(-pi/2) bit. Here’s a derivation.
C = j^j
ln© = ln(j^j) = j \* ln(j)
but
ln(j) = j\*pi/2
so
ln© = -pi/2
C = exp(-pi/2)
**panamajack** , when I first derived it myself, I got the same answer as you. Maybe it’s a branch cut issue?
---
### Author:  [@jcgmoi](https://boards.straightdope.com/u/jcgmoi)
#### Post date: [November 10, 2000, 6:51pm UTC](https://boards.straightdope.com/t/math-two-exponent-questions/40358/22 "2000-11-10T18:51:56Z")
Take special case of Euler’s formula:
e[sup]i\*pi[/sup] = -1
Take square root:
e[sup]i\*pi/2[/sup] = i
Raise to power of i:
esup\*i[/sup] = i[sup]i[/sup]
So e[sup]-pi/2[/sup] = i[sup]i[/sup]
That is, the imaginary unit i, raised to the power of i is a real number.
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### Author:  [@panamajack](https://boards.straightdope.com/u/panamajack)
#### Post date: [November 10, 2000, 9:25pm UTC](https://boards.straightdope.com/t/math-two-exponent-questions/40358/23 "2000-11-10T21:25:09Z")
I wrote :
> [@](#):
>
> Am I missing something?
Why yes, I am, one more j to be precise. I figured the angle for ln j but failed to use Euler’s Formula correctly.
so ln j = **j** \* pi/2 which yields the correct answer,
exp(-pi/2) for j[sup]j[/sup] for the method I showed. Though jcgmoi did it cleanly (and right the first time).
Dr. Matrix, Euler’s formula is :
e[sup]j\*theta[/sup] = cos(theta) + j sin(theta)
It actually is a pretty simple formula if you understand what’s behind it, though I probably shouldn’t try and explain it right now considering how I mishandled it earlier.
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### Author:  [@RickG](https://boards.straightdope.com/u/RickG)
#### Post date: [November 10, 2000, 9:36pm UTC](https://boards.straightdope.com/t/math-two-exponent-questions/40358/24 "2000-11-10T21:36:26Z")
What is it with you engineers using _j_ for the square root of -1? As all good mathematicians and physicists know, the **correct** notation is _i_.
Now off to Great Debates to reside with the Java/C Curly Bracket Position War. 🙂
Rick
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