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Last updated date: 02nd Dec 2023
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MVSAT Dec 2023

What is $ \ln ({i^2}) $ ?

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Hint: The question is given as a logarithmic identity. The I here is the imaginary component which has the value $ \sqrt { - 1} $ .
To find out the solution, solve the bracket first and then come to the natural log.

Complete step-by-step answer:
As we know that,
Natural log: It is the logarithmic function which has the base equal to mathematical constant e.
i is the imaginary component of complex numbers.
I has the value = $ \sqrt { - 1} $
Given in the question,
= $ \ln ({i^2}) $
  i = \sqrt { - 1} \\
  {i^2} = ( - 1) \;
So the question becomes,
= $ \ln ( - 1) $
If we take complex number into considerations
 $ \ln ({i^2}) = i\pi $
Otherwise undefined.

Note: Complex numbers play an important part in calculating ln(-1). If not for the consideration of complex number and rotation in complex plane the answer of the question is undefined. There is no real value exists