Why is my time domain interpolation via zero-padding in frequency domain wrong?

Here is your code with MG's fix applied. A few other tweaks, and a fluffy cloud. The pics look fine to me. Command line Python 2.7

import numpy as np
import matplotlib.pyplot as plt

# odd dimension for simplicity
n    = 19
npad = 299

duration = 0.85*2.0*np.pi
x    = np.arange(0., duration, duration/n)
xpad = np.arange(0., duration, duration/npad)

f = np.cos(x) + 1j*np.sin(x)

f_fwd = np.fft.fft(f)

f_fwd_pad = np.zeros(npad,dtype=complex)

h = (n-1)/2
h = n - 3
f_fwd_pad[0:h+1]   = f_fwd[0:h+1]
f_fwd_pad[npad-h:] = f_fwd[n-h:]

f_interpolated = np.fft.ifft(f_fwd_pad)*npad/n

fig, ax = plt.subplots(1,2)

ax[0].plot(x,np.real(f),marker='x',color='k')
ax[0].plot(xpad,np.real(f_interpolated),color='r')

ax[1].plot(x,np.imag(f),marker='x',color='k')
ax[1].plot(xpad,np.imag(f_interpolated),color='r')

plt.show()

plt.plot( np.real(f_interpolated), np.imag(f_interpolated) )
plt.show()

The answer above is correct. Just to clarify a bit further, using x = np.linspace(0,10,5) will produce 5 numbers from 0 to 10 inclusively

np.linspace(0,10,5)
array([ 0. ,  2.5,  5. ,  7.5, 10. ])

You don't want the last number because in your example the last number is the first number of the next period. A correct implementation would be:

periods = 4.*np.pi
x    = np.arange(0., periods, periods/n)
xpad = np.arange(0., periods, periods/npad)

Your problem is here:

x    = np.linspace(0.,4.*np.pi,n)

The period should be N+1 samples from 0 to 2pi, for n=0..N. Then take x(k) for k=0..N-1

Currently your FFT is not a pure single tone, because the sinusoid does not have a perfect period within the FFT period. And so padding with zeros would not be the correct padding. The fix above will a perfect period within the FFT period, to make padding with zero the correct padding.