BUG: Display precision doesn't affect complex float numbers #25514
- [x] closes #25514
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=h1) Report
> Merging [#25745](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/65c0441a41b2dcaeebb648274d30978419a8661a?src=pr&el=desc) will **decrease** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/25745/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #25745      +/-   ##
==========================================
- Coverage   91.25%   91.25%   -0.01%     
==========================================
  Files         172      172              
  Lines       52977    52979       +2     
==========================================
+ Hits        48343    48344       +1     
- Misses       4634     4635       +1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.82% <100%> (ø)` | :arrow_up: |
| #single | `41.74% <50%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.79% <ø> (ø)` | :arrow_up: |
| [pandas/io/formats/format.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvZm9ybWF0LnB5) | `98% <100%> (ø)` | :arrow_up: |
| [pandas/util/testing.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvdGVzdGluZy5weQ==) | `88.98% <0%> (-0.1%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=footer). Last update [65c0441...0e1f3b6](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=h1) Report
> Merging [#25745](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/e02ec8f89a743cc56a79e660b7be850448d15f61?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/25745/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #25745      +/-   ##
==========================================
- Coverage    91.9%   91.89%   -0.02%     
==========================================
  Files         175      175              
  Lines       52485    52501      +16     
==========================================
+ Hits        48235    48244       +9     
- Misses       4250     4257       +7
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.44% <100%> (-0.01%)` | :arrow_down: |
| #single | `40.73% <27.27%> (-0.16%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `96.79% <ø> (-0.12%)` | :arrow_down: |
| [pandas/io/formats/format.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvZm9ybWF0LnB5) | `97.91% <100%> (+0.01%)` | :arrow_up: |
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `75% <0%> (-12.5%)` | :arrow_down: |
| [pandas/core/sparse/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc3BhcnNlL2ZyYW1lLnB5) | `95.5% <0%> (-0.2%)` | :arrow_down: |
| [pandas/compat/\_\_init\_\_.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2NvbXBhdC9fX2luaXRfXy5weQ==) | `77.5% <0%> (-0.15%)` | :arrow_down: |
| [pandas/plotting/\_core.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb3JlLnB5) | `83.77% <0%> (-0.09%)` | :arrow_down: |
| [pandas/core/computation/expr.py](https://codecov.io/gh/pandas-dev/pandas/pull/25745/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vZXhwci5weQ==) | `96.7% <0%> (ø)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=footer). Last update [e02ec8f...3fd69e9](https://codecov.io/gh/pandas-dev/pandas/pull/25745?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 does this also change the notebook display? if so can we have a test for to_html() with notebook =True and False. can you merge master and see if you can update > can you merge master and see if you can update

Done. thanks @sakarpanta 