Complex Analysis: Theory and Applications · Problem 5.2.3

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · complex-logarithm-equations

Problem

Find all the values of

z

for which each equation holds. ((a))

\mathrm{Log}(z) = 1 - i\frac{\pi}{4}

. ((b))

\mathrm{Log}(z-1) = i\frac{\pi}{2}

. ((c))

\exp(z) = -ie

. ((d))

\exp(z+1) = i