You can't find the amplitude of √3 - i. You can find the radius and angle of that expression, applying the Euler's formula.
√3 - i = rcos(θ) + irsin(θ)
Well...
√3 = rcos(θ)
-1 = rsin(θ)
Then:
r = 2, which gives us:
cos(θ) = √(3)/2
sin(θ) = -½
So = -π/6
Therefore, the radius if 2 and the angle is -π/6 radians.
* * * * *
The amplitude = θ = -π/6