Question

Find the general value of ${log}_e$(i).

• A. n I
• B. n I
• C. n I
• D. n I

Answer 1

The correct option is C

n I

Convert complex number in Euler's form

${log}_e$(i)

= ${log}_e$ $[cos\frac{\pi }{2}+isin\frac{\pi }{2}]$

= ${log}_e$ $\left[e^{i\frac{\pi }{2}}\right]$

= $\frac{i\pi }{2}$ + 2n $\pi$ i n $ϵ$ I

= $\frac{i\pi (4n+1)}{2}$ n $ϵ$ I