urgent help in logarithm

Apr 2010
43
0
Find all values of the logarithm of each of the following numbers and state in each case the principal value. Put your answer in the form a+ib.
(a) -sqrt(
3) + i
this is what i done but dont know if correct and dont know how to continue so please help!

log(-sqrt(3) + i )= Log(2) + i(-pi/6 + 2kpi)

but what is the principal value and is it in the form of a + ib

(b) e^i

log(e^i)= i + i(2kpi) = i( 1+ 2kpi)
???
and also what are the principal values and the form of a + ib
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
Find all values of the logarithm of each of the following numbers and state in each case the principal value. Put your answer in the form a+ib.​


(a) -sqrt(3) + i
this is what i done but dont know if correct and dont know how to continue so please help!

log(-sqrt(3) + i )= Log(2) + i(-pi/6 + 2kpi)

but what is the principal value and is it in the form of a + ib

(b) e^i

log(e^i)= i + i(2kpi) = i( 1+ 2kpi)
???
and also what are the principal values and the form of a + ib
Principle value: k = 0.

But you should be consulting your classnotes or textbook on this.
 
Apr 2010
43
0
Principle value: k = 0.

But you should be consulting your classnotes or textbook on this.
The lecturer didnt really explain this well and not clear lecture notes so is what i done correct and the only thing is that k=0 for both parts a) and b) ????????????
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
The lecturer didnt really explain this well and not clear lecture notes so is what i done correct and the only thing is that k=0 for both parts a) and b) ????????????
Yes.