DataFrame.interpolate() failes with complex dtype

[jennirinker]

MWE

import numpy as np
import pandas as pd

df = pd.DataFrame(np.random.rand(3,2), dtype=complex)
df.iloc[1,:] = np.nan
print(df)
print()
print(df.interpolate())

Problem description

Calling interpolate() on a pandas dataframe with complex data returns the same dataframe, still with NaNs present. It would be nice if pd.interpolate() either
a) copied NumPy's interpolation functionality for complex numbers or
b) threw a warning that interp doesn't work for complex numbers

Expected Output

I would expect the interpolate method to replace the NaNs in my dataframe with the lineraly interpolated values.

Output of pd.show_versions()

[paste the output of pd.show_versions() here below this line]
INSTALLED VERSIONS

commit: None
python: 3.6.1.final.0
python-bits: 64
OS: Windows
OS-release: 7
machine: AMD64
processor: Intel64 Family 6 Model 78 Stepping 3, GenuineIntel
byteorder: little
LC_ALL: None
LANG: en
LOCALE: None.None

pandas: 0.20.3
pytest: 3.2.1
pip: 9.0.1
setuptools: 27.2.0
Cython: 0.25.2
numpy: 1.13.1
scipy: 0.19.0
xarray: 0.9.6
IPython: 6.1.0
sphinx: 1.6.3
patsy: None
dateutil: 2.6.0
pytz: 2017.2
blosc: None
bottleneck: None
tables: 3.2.2
numexpr: 2.6.2
feather: None
matplotlib: 2.0.2
openpyxl: 2.4.8
xlrd: 1.0.0
xlwt: 1.3.0
xlsxwriter: 1.0.0
lxml: None
bs4: None
html5lib: 0.999
sqlalchemy: 1.1.13
pymysql: None
psycopg2: None
jinja2: 2.9.6
s3fs: None
pandas_gbq: None
pandas_datareader: None

[jreback]

we have very little testing for complex dtypes. welcome to add tests and implementatoins!

[jreback]

note that #17927 may also be at play here

[mroeschke]

This looks to work on main now and is tested so closing