Abstract
As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to derive suitable formulas from these methods. In this paper, we present a novel way to compute the powers of an octonion number using formulas derived from the binomial expansion.
Highlights
An octonion number a can be expressed as:a =a0 + a1i1 + a2i2 + a3i3 + a4i4 + a5i5 + a6i6 + a7i7 (1)where a0, a7 are real numbers and i1,i7 are imaginary units
We present a novel way to compute the powers of an octonion number using formulas derived
We use a new technique to construct formulas computing the powers of an octonion
Summary
An octonion number a can be expressed as:. where a0 , , a7 are real numbers and i1, ,i7 are imaginary units. An octonion number a can be expressed as:. Where a0 , , a7 are real numbers and i1, ,i7 are imaginary units. An octonion a can be represented by 8×8 real matrices. The problem of computing the nth power of an octonion is still interesting to many researchers. Some methods are used, such as binomial expansion, De Moivre’s formula, and Euler’s formula. To solve this problem, we use a new technique to construct formulas computing the powers of an octonion
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