Solving an Equation: Rearranging Numbers Around

[xvtsx]

Homework Statement

Okay, yesterday in class my teacher gave me this identity $$e^{i\pi }+1=0$$
and she wants me to rearrange the numbers around, so I can get this $$i^{i}= e^{-\frac{\pi}{2}}$$

Homework Equations

and

The Attempt at a Solution

I know that if Isolate the 1 to the other side and take the square root of each sides I will have this $$\sqrt{e^{i\pi }}= \sqrt{-1}$$
But this is the question what do I do after that ?

 

[jbunniii]

Homework Equations

and

The Attempt at a Solution

I know that if Isolate the 1 to the other side and take the square root of each sides I will have this $$\sqrt{e^{i\Pi }}= \sqrt{-1}$$
But this is the question what do I do after that ?

Do you know another way to write

$$\sqrt{e^{i \pi}}$$?

Do you know another way to write

$$\sqrt{-1}$$?

 

[tiny-tim]

Hi xvtsx!

(have a pi: π and try using the X² tag just above the Reply box )

Raise each side of your last equation to the power of i.

 

[xvtsx]

Hmm.. do I raise to the power of i after I change the square root for $$\frac{1}{2}$$ and multiple it with $$iπ$$ ?

 

[tiny-tim]

(what happened to that π i gave you? )

Yes, (e^iπ/2)ⁱ = … ?

 

[xvtsx]

sorry for the pi part, but I use the latex editor and it only gaves that one xD.. thanks by the way. :)