Complex number need an idea to start

naspek
Messages
176
Reaction score
0

Homework Statement



Find the principal value of i^2i

Homework Equations



principal value = Ln r + iArg(z)

The Attempt at a Solution


dont know how to start..
 
Physics news on Phys.org
Hint: i^{2i} = e^{2i\ln{i}}
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Where is ##(z+1)Ln(z)## differentiable?
Replies
5
Views
2K
[Complex analysis] Contradiction in the definition of a branch
Replies
8
Views
2K
Find the complex number which satisfies the given equation
Replies
6
Views
2K
Complex logarithm as primitive
Replies
13
Views
2K
Partial fractions with complex linear terms
Replies
8
Views
991
Order of Zero of Complex Logarithm
Replies
5
Views
2K
Fundamental matrix for complex linear DE system
Replies
4
Views
1K
Solve integral by finding Fourier series of complex function
Replies
3
Views
1K
Complex Number Modulus and Argument Calculations
Replies
9
Views
5K
Finding analyticity of a complex function involving ln(iz)
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top