双四元数（复化四元数）-1的根
Biquaternion (complexified quaternion) roots of -1
摘要：
研究了双四元数（含复分量的四元数，或含四元数实部和虚部的复数）集合中-1的根，证明了存在无穷多个非平凡复化四元数根（以及复虚算子和单位纯实四元数集合的两个退化解）.证明了非平凡根由纯四元数实部和虚部垂直的复数组成。两个正交的纯四元数的模可以通过双曲三角恒等式用单个参数表示。
英文摘要：
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.
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