A number is purely imaginary if it can be expressed in the form \( bi \), where \( b \) is a real number and \( i \) is the imaginary unit.
From the options you provided:
- 3 is a real number.
- 4i is purely imaginary (where \( b = 4 \)).
- 5 + 2i has a real part (5), so it is not purely imaginary.
- 0 is considered neither purely real nor purely imaginary.
Therefore, the purely imaginary number from the options is 4i.