Calculating $Log(-e i)$

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$$Log(-e i)$$

My try:

$$=\ln|0+(-e)i|+i[\arg (0+(-e i))+2\pi k]$$

$$=\ln|e i|+i(-\frac{\pi}{2}+2\pi k)$$

My attempt is correct?

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2 Answers

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$$...=\ln(|i||e|)$$

$$=\ln(|i|)+\ln(|e|)$$

$$=\ln(1)+\ln(|e|)$$

$$=0+1$$

$$\Longrightarrow \boxed{1+i(-\frac{\pi}{2}+2 \pi k)}$$

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Correct but incomplete. The absolute value of ei is e, and the ln of that is 1.

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