Question

The value of log (- x) in complex form is​

Answer 1

Answer:

The complex logarithm of -x can be written as log (-x) = log |x| + i * (π + arg x).

Step-by-step explanation:

From the above question,

They have given :

The complex form of the logarithm of a negative number is not defined, as the logarithm of a negative number is not real. However, the logarithm of a complex number can be expressed in terms of the natural logarithm and the imaginary unit "i". The complex logarithm of a complex number is defined as:

ln(z) = ln|z| + i * arg(z)

Where |z| is the magnitude of the complex number, arg(z) is the argument of the complex number, and ln is the natural logarithm.

The logarithm of a negative number is not defined in real numbers, but it can be defined in the complex plane.

The complex logarithm of a complex number is multi-valued, meaning that there are infinitely many values of the logarithm that differ by multiples of 2πi.

The complex logarithm of -x can be written as,

          log (-x) = log |-x| + i * arg (-x),

Where |-x| is the magnitude of -x and arg (-x) is its argument.

The magnitude of -x is equal to |x|, and the argument of -x can be expressed as π + arg x, where arg x is the argument of x.

So,

   The complex logarithm of -x can be written as log (-x) = log |x| + i * (π + arg x).

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