Final answer:
The statement is true because a non-zero complex number, such as one that results in 3i when raised to the fourth power, always has a multiplicative inverse, rendering it invertible.
Step-by-step explanation:
The statement 'If a4 = 3i, then a is invertible' is true. In the context of complex numbers, if a is raised to the power of 4 and equals a non-zero complex number, it implies that a itself is a non-zero complex number. By definition, a non-zero complex number is always invertible because there exists a multiplicative inverse such that a multiplied by its inverse gives the multiplicative identity (1).