This is a test of your knowledge in mathematics?

Question

We all know the very famous Euler's Identity
e^iπ + 1 = 0

Now, we transpose 1
e^iπ = -1

We raise both sides to 2
e^2iπ = 1

Now, we raise both sides to the power 1/2iπ.
e^(2iπ/2iπ) =1^(1/2iπ)

Therefore,
e^1 = 1

And,
e = 1

Happy?
^_^

Answer 1

Your equation e^2iπ = 1 is fine. Your mistake is assuming after the next equation that 1^(1/2iπ) must be 1.

To evaluate 1^x, i.e. to solve 1^x = y, we need to find a value y such that raising it to the power 1/x gives us 1. Certainly, y = 1 will always work, but your other equation e^2iπ = 1 is staring you in the face telling you that other quite unexpected values of y will also work for certain powers. Ignoring this case has given you your impossible conclusion.

Answer 2

I can't debate this as I'm not a math major, however after reading the wikipedia article titled "euler's identity" I find that some of your work seems to be off. As π can be calculated somewhat. I don't think this problem is a simple algebra problem as your calculation makes it.

Answer 3

that happened the moment you transposed 1 the rest is smoke and mirrors

Answer 4

Im returning the question What does it mean???

Answer 5

raise both sides to two....the second step....it looks suspect to me.

Answer 6

umm math is hard and if you say its right i agree

Answer 7

I flunked that one.

Answer 8

where is the fallacy?

Answer 9

Please be clear about ur question.