What calculate ln &#x2061;<!-- ⁡ --> i I would like to know how to calculate ln

Joshua Foley 2022-07-08 Answered
What calculate ln i
I would like to know how to calculate ln i. I found a formula on the internet that says
ln z = ln | z | + i Arg ( z )
Then | i | = 1 and Arg ( i ) is?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Asdrubali2r
Answered 2022-07-09 Author has 14 answers
If you want to know what is ln i you should make yourself aware of what the result should be. By definition the logarithm of i should be some complex number z such that e z = i. But by Euler's formula e i π / 2 = cos ( π / 2 ) + i sin ( π / 2 ) = i, so you could say that " ln i = i π / 2". And that is true if we choose ln to be the principal branch of the complex logarithm.
But be aware that since the exponential function is periodic, also e i π / 2 + 2 π i k = i holds for all k Z . Therefore the logarithm is a multi-valued function.
Did you like this example?
Subscribe for all access
Bruno Pittman
Answered 2022-07-10 Author has 4 answers
Given any non-zero complex number z , Arg ( z ) (the principal argument of z) is the unique θ ( π , π ] such that z = | z | e i θ . Observing that θ gives a radian measure of rotation from the positive real axis, what must the principal argument of i be, that is, how much must we rotate | i | = 1 to get it to i again?
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-04-02
Exponential and logarithmic series: Find the sum of
22+322!+423!+ to infinity
asked 2021-11-20
Please, solve this for me:
ln(1)=iπ;
and ln(x)=lnx+iπ for x>0 and xR
asked 2022-06-22
How can I solve the equation...
log ( π i 1 π i ) = k = 0 K x i k β k i = 1 , 2 , , N
How can I make the equation above the one below by taking " e" to both sides.
Note that after taking e to both sides of Eq. 1,
π i 1 π i = e k = 0 K x i k β k .
Thank you in advance.
asked 2022-06-24
Integral 0 1 ln x x 2 + 1 ln ( 3 x 2 + 1 x 2 + 3 ) d x
I need to evaluate the following integral:
0 1 ln x x 2 + 1 ln ( 3 x 2 + 1 x 2 + 3 ) d x .
Could you suggest how to find a closed form for it? I am not sure if there is one, but the integrand seems simple enough, so I hope it might exist.
asked 2022-04-30
Solve for y: log 4  ( 4 7 y ) = 3.
asked 2022-11-20
Is 1 + lg i = lg ( i + i )?
I've been studying Sedgewick's "Algorithms" book and in proof of one proposition he writes the following:
the property is preserved because
1 + lg i = lg ( i + i ) lg ( i + j ) = lg k
I cannot wrap my brain around the first part of this inequation, namely 1 + lg i = lg ( i + i ). Can anyone offer an explanation? Thanks in advance!
asked 2021-08-19
Please, write the logarithm as a ratio of common logarithms and natural logarithms.
log5(86)
a) common logarithms
b) natural logarithms