Reproduction depends on the quoting.

QUOTE_ALL

import csv
data = [1, 1j]
with open('example.csv', 'w') as f:
    writer = csv.writer(f, quoting=csv.QUOTE_ALL)
    writer.writerow(data)

with open('example.csv') as f:
    contents = f.read()
    print(contents)  # 1,1j
    reader = csv.reader(contents, quoting=csv.QUOTE_ALL)
    print(list(reader))  # [['1'], ['', ''], ['1'], ['j'], []]

In this case, we don't have our data back, but at least it does not raise.

QUOTE_NONNUMERIC

Qouting docs:

No automatic data type conversion is performed unless the QUOTE_NONNUMERIC format option is specified (in which case unquoted fields are transformed into floats)

import csv
data = [1, 1j]
with open('example.csv', 'w') as f:
    writer = csv.writer(f, quoting=csv.QUOTE_NONNUMERIC)
    writer.writerow(data)

with open('example.csv') as f:
    contents = f.read()
    print(contents)  # 1,1j
    reader = csv.reader(contents, quoting=csv.QUOTE_NONNUMERIC)
    print(list(reader))

# Traceback (most recent call last):
#   File "/Users/sobolev/Desktop/cpython/ex.py", line 11, in <module>
#     print(list(reader))
#           ^^^^^^^^^^^^
# ValueError: could not convert string to float: 'j'

In this case, it raises an error, while trying to convert 1j to float.

Current docs / tests

I cannot find any mentions of complex numbers in tests or docs for csv.

Solutions?

1. We can say that it works as expected: with this strange QUOTE_ALL formatting and QUOTE_NONNUMERIC exception. Add a test case for it and forget about it
2. We can try to quote complex as string: in this case it will be treated as "1j". I think it is much better, because it will allow users to convert this value to complex manually
3. Forbid writting complex numbers. However, I don't think it is a path we should go