I know that with base e you use the natural log of complex numbers rule...(adsbygoogle = window.adsbygoogle || []).push({});

ln(x+yi) = ln|x| + arcsin(y/x)i

...because the limit e somehow corresponds to radians about the unit circle

thus, when you take ln(-1) you can do

ln(-1 + 0i) = ln|-1| = arsin(0/-1)i

ln(-1) = 0 + pi*i

ln(-1) = pi*i

My first question is this: What is the relationship between the limit e as the log's base and the unit circle with respect to complex answers?

My second question: How do you find the log of a negative number when the base is not the limit e?

aside... it just dawned upon me while typing this that i might be able to jsut devide the complex answer by the ln of the desired base? such that...

logb(-1) = ln|-1|/ln(b) + arctan(0/-1)i/ln(b)

logb(-1) = logb|-1| + [1/ln(b)][arctan(0/-1)]i

is that the proper way to do this?

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# Homework Help: Logs of negative numbers (any base)

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