Question

What Ln(z) is answer????!!

Answer 1

Write z in exponential form:

$z=1-i=\sqrt2 e^{-i\frac\pi4}$

Then taking the logarithm, we get

$\mathrm{Ln}(z)=\ln(\sqrt2) + \ln e^{-i\frac\pi4} = \boxed{\ln(\sqrt2)-\dfrac\pi4i}$

so a is the correct answer.