The discussion focuses on solving the complex equation involving the expression zc = ec log(z) and the manipulation of logarithmic identities. The user attempts to simplify the equation by substituting c = 0.5 - i and z = i, leading to the expression zc = e(0.5 - i) log(i). The conversation highlights the challenge of applying the second equation, z^(1/n) = exp[(1/n) log(z)], to the term e^(-i log(i)). A key suggestion is to explore the possible values of log(i) to progress further in the solution.
PREREQUISITESStudents studying complex analysis, mathematicians working with logarithmic identities, and anyone tackling advanced algebraic equations involving complex numbers.
alexcc17 said:Homework Statement
i.5 - i
Homework Equations
zc=ec log(z)
z1/n=exp[(1/n) log(z)], n is in integer
The Attempt at a Solution
letting c=.5-i and z=i so
zc=e(.5-i) log(i) = e.5 log(i)*e-i log(i)
from the second equation I reduced it to:
i.5*e-i log(i) but I'm not sure where to go from there since the second known equation doesn't apply to the e^(-i log(i)) part