The document presents the solution for the complex expression z = e^(1-i/3), which is derived by separating the real and imaginary parts using Euler's formula. It calculates e^(-i/3) as 1/2 - i(√3/2). The real part is e/2 and the imaginary part is -e(√3/2).

1. z= e^(1-i/3) = e.e^(-i/3)
we know that e^-ix = cos x - i sin x
so e^(-i/3) = cos /3 - i sin/3 = 1/2 - i3 /2
real part of e.e^(-i/3) = e/2
imaginary part = - e3 /2
Solution
z= e^(1-i/3) = e.e^(-i/3)
we know that e^-ix = cos x - i sin x
so e^(-i/3) = cos /3 - i sin/3 = 1/2 - i3 /2
real part of e.e^(-i/3) = e/2
imaginary part = - e3 /2