Chapter 12.7, Problem 16E

To determine

To find: the value to four decimal places.

Answer to Problem 16E

  $i\pi -3.4112$

Explanation of Solution

Given information:

  $\ln \left(-0.033\right)$

Calculation:

Use $\ln \left(ab\right)=\ln \left(a\right)+\ln \left(b\right)$ to evaluate the given value as follows:

  $\begin{array}{c}\ln \left(-0.033\right)=\ln \left(-1\times 0.033\right)\\ =\ln \left(-1\right)+\ln \left(0.033\right)\\ =i\pi -3.4112\end{array}$

Thus, the value is $i\pi -3.4112$ .