Question: how to calculate log of a negative number?
Answer: In particular, the logarithm of a negative real number x can then be calculated as log(x)=log(|x|eiπ)=log(|x|)+log(eiπ)=log(|x|)+iπ. for all k∈Z. Therefore, the complex logarithm is only defined up to multiples of 2πi ! or maybe log(x)=log(|x|e−i1772π)=log(|x|)+log(e−i1772π)=log(|x|)−i1772π.