# B Implications of e^i*pi = -1

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1. Aug 17, 2016

### Anonymous Vegetable

Before I start, there are only really two pieces of information this concerns and that is the idea that 1x = 1 and that ei*π = -1

So it would follow that (ei*π)i = -1i
And so that would mean that i2i = e which doesn't seem to be right at all. Where is the issue here as there must be one but I am sure I don't have the knowledge required to figure it out.

2. Aug 17, 2016

### Bystander

Re-investigate this aspect.

3. Aug 17, 2016

### Anonymous Vegetable

I've edited it to make another point anyway hahaha but yeah I shall

4. Aug 17, 2016

### Bystander

Point of order: please do NOT make changes to your original post. It makes very confusing reading for late arriving participants.

5. Aug 17, 2016

### Anonymous Vegetable

My humbumblest apologies and it shan't happen again.

6. Aug 17, 2016

### Staff: Mentor

7. Aug 17, 2016

### Bystander

De nada. You're new to the forum.

8. Aug 17, 2016

### Staff: Mentor

Not all exponentiation laws work with complex numbers, and with a complex base those exponents are not unique any more.

$$i^{2i} = e^{2i \log(i)} = e^{2i (i \pi/2)} = e^{- \pi}$$ using the principal value of the logarithm, indeed.

9. Aug 17, 2016

### Anonymous Vegetable

10. Aug 17, 2016

### Anonymous Vegetable

I just find it amusing that what appears to be an extremely non real value seems to equal a simple real number

11. Aug 17, 2016

### Anonymous Vegetable

I assume your log refers to ln? Sorry just being picky

12. Aug 17, 2016

### micromass

Staff Emeritus
Outside of high school, logarithms with base $e$ are always denoted as $\log$. The notation ln is not really used anymore.

13. Aug 17, 2016

### Staff: Mentor

I don't believe that's true. Every calculus textbook I have distinguishes between log (meaning base-10 logarithm) and ln. Granted, all of my textbooks are at least 15 to 20 years, and some are older.

14. Aug 21, 2016

### Battlemage!

I know it adds little to the conversation, but I have to concur. Pretty much all my textbooks use ln. Maybe it's an undergrad thing?

15. Aug 22, 2016

### Isaac0427

What seems to be the problem? I don't see one.