Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce complexity as kuhm-PLEHK-suh-tee (/kəmˈplɛksəɾi/). In "complexity", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, a hallmark of natural-sounding American speech. It comes out as kuhm·PLEHK·suh·tee. Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "I appreciate the complexity of the musical arrangement" or "The trial lasted for three weeks due to the complexity" — more examples below.
Record yourself saying "complexity" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 11 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Press your lips together to stop the air, then release. No vocal cord vibration.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "complexity", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
Stress falls on the second syllable, not the others. Stretch PLEHK — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.