How Does the Principal Argument Affect the Solution of Log(exp(10i))?

[NewtonianAlch]

Homework Statement

Log(exp(10i))

The Attempt at a Solution

Since we want to get this in terms of the principal argument, would it matter if we ultimately wrote i(10 - 3$\pi$) or i(10 - 4$\pi$), since they are both in range?

 

[jambaugh]

Yes it matters. i(10 - 3pi) is not a full cycle difference, so not an equivalent angle.

 

[NewtonianAlch]

Thanks!