then, `sqrt(complex(a))`

?

from the help `?sqrt`

:

```
sqrt(A::AbstractMatrix)
If A has no negative real eigenvalues, compute the principal matrix square root of A, that is the unique matrix X with eigenvalues having
positive real part such that X^2 = A. Otherwise, a nonprincipal square root is returned.
If A is symmetric or Hermitian, its eigendecomposition (eigen) is used to compute the square root. Otherwise, the square root is determined
by means of the Björck-Hammarling method [^BH83], which computes the complex Schur form (schur) and then the complex square root of the
triangular factor.
```