What calculate ln ⁡ iI 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?

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What calculate   ln  ⁡  iI 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?

Asdrubali2r · Accepted Answer

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&#039;s formula       e          i      π              /            2        =  cos  ⁡  (  π      /    2  )  +  i  sin  ⁡  (  π      /    2  )  =  i, so you could say that &quot;  ln  ⁡  i  =  i  π      /    2&quot;. 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.

Bruno Pittman · Accepted Answer

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?

What calculate ln ⁡ i I would like to know how to calculate ln

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