The principal value of ln(1 + i) represents the natural logarithm of the complex number (1 + i).
To calculate it, first, we need to convert the complex number into polar form:
1 + i = √(1^2 + 1^2) * (cos(π/4) + i * sin(π/4))
Now, the principal value of ln(1 + i) is:
ln(1 + i) = ln(√2 * (cos(π/4) + i * sin(π/4)))
Since ln(r * e^(iθ)) = ln(r) + iθ, where r is the magnitude and θ is the angle in the polar form, we get:
ln(1 + i) = ln(√2) + i * (π/4)
So, the principal value of ln(1 + i) is ln(√2) + i * (π/4).