1. Find all the values of log(1-i) , log(3-2i)

Question

2. Find all the values for the following expressions.
(a) 5^i 1 (b) log(1+i)^πi

Answer 1

1-i = √2 e^(-π/4 i)
so, log(1-i) = 1/2 log2 - (π/4 +2kπ)i

Do 3-2i in like wise

5^i = e^(ln5 i) = cos ln5 + i sin ln5
log(1+i)^(πi) = πi log(1+i) = πi (1/2 log2 + π/4 i) = -π^2/4 + π/2 log2 i

Answer 2

Math