Question

What is the exact value of Ln I ?

Answer 1

Is that supposed to be an "I" or a one?

Answer 2

a I

Answer 3

not a one :p

Answer 4

If you know about the complex exponential it follows the following identity, because when dealing with complex and imaginary numbers the exponential and trig functions are closely tied to one another :
\[e ^{i*x}=\cos(x)+i*\sin(x)\] where x is measured in radians... so:
\[e ^{i*\frac{ \pi }{ 2 }}=\cos(\frac{ \pi }{ 2 }) + i*\sin(\frac{ \pi }{ 2 })=i\]So the natural logarithm of i must be:
\[\ln(i) = i*\frac{ \pi }{ 2 } = \frac{ i*\pi }{ 2 }\]

Answer 5

but the answers just say -1, 0, e, and 1