Why are there infinitely many values if a complex number

Winigefx

Winigefx

Answered question

2022-06-14

Why are there infinitely many values if a complex number is raised to an irrational power?

Answer & Explanation

Patricia Curry

Patricia Curry

Beginner2022-06-15Added 15 answers

If a , b C and a 0, then a b is any number of the form exp ( b log a ), where log a is any logarithm of a. But if l a is one logarithm of a, then
{ logarithms of  a } = { l a + 2 π i m | m Z } .
So, if b is irrational and if m n, then
exp ( b ( l a + 2 π i m ) ) exp ( b ( l a + 2 π i n ) ) .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?