  The roots of -1 in the set of biquaternions (quaternions with complex
components, or complex numbers with quaternion real and imaginary parts) are
studied and it is shown that there is an infinite number of non-trivial
complexified quaternion roots (and two degenerate solutions which are the
complex imaginary operator and the set of unit pure real quaternions). The
non-trivial roots are shown to consist of complex numbers with perpendicular
pure quaternion real and imaginary parts. The moduli of the two perpendicular
pure quaternions are expressible by a single parameter via a hyperbolic
trigonometric identity.
