I guess some very basic parametrization (for circles, ellipses, lines and similar) is useful to. Example: The lines in Sanae's stars.

As Drake said, don't make mathematically complex patterns that aren't fun to play (but come on, that Daiyousei script isn't that bad) for the sake of making mathematically complex patterns. I say make maths for the patterns, not patterns for the maths (if that makes any sense to you). That is, come up with the patterns first, then do the maths.

Often, you can use bullet manipulations that don't require much maths (bullets changing speeds, bullets changing angles, bullets spawning more bullets, bullets bouncing off walls, etc.) to improve/vary your patterns instead of using a lot of maths. Of course, this requires some programming skills, but you can make great patterns even with nothing but basic object bullet manipulation.

On the other hand, remember that complex doesn't imply bad either. If you have a mathematically complex pattern that fits the enemy/boss and is fun to dodge, feel free to use it.

Also, simple =/> good and simple =/> bad (here, "simple" covers both mathematical and programming-wise simplicity). Many fairly simple patterns work well, but overly simple patterns, particularly when used by bosses (example: All the boss ever does is firing random rings of 30 blue bullets.), are often considered bland and uninspired.