Question

principal value of log (-3)​

Answer 1

Answer:

Not possible

Step-by-step explanation:

Input always be greater than zero.

Answer 2

Principal value of log (-3) is log(3) + πi

Given :

The function log (-3)

To find :

The principal value of log (-3)

Solution :

Step 1 of 2 :

Write down the given function

The given function is log (-3)

Step 2 of 2 :

Find principal value of log (-3)

We know that

$\sf log( - 1) = \pi i + 2k\pi i\: \: \: where \: k \in \mathbb{Z}$

Thus we get

log (-3)

= log (3 × - 1)

= log(3) + log( - 1)

$\sf = log( 3) + \pi i + 2k\pi i\: \: \: where \: k \in \mathbb{Z}$

Hence the required principal value of log (-3)

= log(3) + πi

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