Question

Given that Sinharch(x)=ln(x+√x^2+1),determine Sinharch(2+j) in the form a+bj

Answer 1

√((2+j)^2+1)=2√(1+j) = 1.197+0.910j

so you want
log(3.197+1.910j)
Now recall that if z=a+bj then log(z) = log|z|+arccos(a/|z|)j