# Complex Logarithm

## Homework Statement

find -Ln(1-e(i$$\theta$$) (in terms of theta)

(this is me just skipping the part of the problem I know and going straight to what I can't figure out)

## Homework Equations

ln(z) = ln(rei$$\theta$$)=Ln(r) + ln(ei$$\theta$$) = Ln(r) + i$$\theta$$

## The Attempt at a Solution

I don't really know how to break this logarithm up into real and complex parts, the two ways I considered were

= -(Ln(1-1) + i$$\theta$$)
but that ends up with Ln(0) which blows up to infinity and doesn't make sense in this problem.

= -(Ln(1) + i$$\theta$$)
but this is just -i$$\theta$$ which leaves only an imaginary part, and the problem implies there is a real logarithmic solution as well.

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