Which angle to use when exponetiating complex numbers ? (What does (-Ï€,Ï€] mean exacly)...e, ln and Ln?

Question

z = x + iy

i is sqrt(-1)

e^(z-1) = -ie^2

This is equal to

z-1 = ln(-ie^2)=log[e](e^2) + i( (3π)/2 + 2nπ)

Which is

2+ i( (3π)/2 + 2nπ)

so z = 3i( (3π)/2 + 2nπ)

Instead of (3i( (3π)/2 + 2nπ) I get (3i( -(π)/2 + 2nπ)

I am not sure what (-π,π] means, but I assume it means pick what angle is closest to 0/2π.

(3π)/2 would contradict this idea.

Can anyone better explain the use of angles and their positive or negative variation in e ln and Ln equation when working with complex numbers...

This is the only problem i found that had this by the way...so could it be an error...

Answer 1

Complex arithmetic is not that difficult. However it is not my expertise. I can tell you this - pi is just an angle of 180 degrees so -pi would be the same angle. the proper term is pi radians. Of course e is a constant and ln or Ln refer to the natural or Napierian logarithms. (Logarithm base e).

Answer 2

E=MC squared

the target ppl here r students students students