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It is known that Clifford (geometric) algebra offers a geometricinterpretation for square roots of -1 in the form of blades that square tominus 1. This extends to a geometric interpretation of quaternions as the sideface bivectors of a unit cube. Research has been done [S. J. Sangwine,Biquaternion (Complexified Quaternion) Roots of -1, Adv. Appl. Cliford Alg.16(1), pp. 63-68, 2006.] on the biquaternion roots of -1, abandoning therestriction to blades. Biquaternions are isomorphic to the Clifford (geometric)algebra $Cl_{3}$ of $\R^3$. All these roots of -1 find immediate applicationsin the construction of new types of geometric Clifford Fourier transformations.  We now extend this research to general algebras $Cl_{p,q}$. We fully derivethe geometric roots of -1 for the Clifford (geometric) algebras with $p+q \leq4$.

Geometric Roots of -1 in Clifford Algebras $\G_{p,q}$ with $p+q \leq 4$