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  • How many roots does the polynomial z^2 + 1 have over the quaternion algebra?

    The polynomial z^2 + 1 has two roots over the quaternion algebra. These roots are complex numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit. In the quaternion algebra, the roots of this polynomial are not only complex numbers but also include elements of the form c + di + ej + fk, where c, d, e, and f are real numbers and i, j, and k are the quaternion units.

  • How many zeros does the polynomial z^2 + 1 have over the quaternion algebra?

    The polynomial $z^2 + 1$ has infinitely many zeros over the quaternion algebra. This is because the quaternion algebra is non-commutative, and thus the polynomial may have non-trivial zero divisors. Specifically, the zeros of this polynomial in the quaternion algebra are of the form $z = ai + bj + ck + d$, where $a, b, c, d$ are real numbers and $i, j, k$ are the quaternion units.

  • How many roots does the polynomial z^2 + 1 have in the quaternion algebra?

    The polynomial z^2 + 1 has two roots in the quaternion algebra. These roots are i and -i, where i is the imaginary unit in the quaternion algebra. The quaternion algebra is a four-dimensional algebra over the real numbers, so the polynomial can have up to two distinct roots.

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    Sensuality, to me, means being fully present in the experience of the senses. It is about savoring the textures, tastes, scents, sounds, and sights that surround us, and allowing them to awaken a deep, visceral pleasure within us. Sensuality is about indulging in the richness of the present moment and allowing ourselves to be fully immersed in the physical and emotional sensations that come with it. It is a celebration of the body, the senses, and the beauty of the world around us.

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