Question

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

Answer 1

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,
= $\ln ({i^2})$
As
$i = \sqrt { - 1} \\\ {i^2} = ( - 1) \;$
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