Algebra Pre-Algebra and Basic Algebra Math Forum

 September 2nd, 2017, 03:42 AM #1 Senior Member   Joined: Nov 2011 Posts: 175 Thanks: 2 formula. please help!!!! In a page of Wikipedia, there is a formula I don't understand. My English is bad English. Please tell me in simple words what the meaning is of: ijk = −1 In the formula, what is i, j and k... Thank your forward. If you could, help me to design this message in better English after you help me in the question. Last edited by skipjack; September 2nd, 2017 at 03:48 AM.
 September 2nd, 2017, 03:42 AM #2 Senior Member   Joined: Nov 2011 Posts: 175 Thanks: 2
 September 2nd, 2017, 04:00 AM #3 Senior Member   Joined: Aug 2017 From: United Kingdom Posts: 119 Thanks: 38 Math Focus: Algebraic Number Theory, Arithmetic Geometry $i$, $j$ and $k$ are just symbols for which the following is true: $i^2 = j^2 = k^2 = ijk = -1$ From this, you can deduce that $ij = -ji = k$, $jk = -kj = i$ and $ki = -ik = j$ These guys appear in various situations. One of the five groups (up to isomorphism) of order 8 is the group $Q_8 = \{\pm 1, \pm i, \pm j, \pm k \}$. There is also the ring $H = \{a + bi + cj + dk \, | \, a, b, c, d \in \mathbb{R} \}$ of quaternions, with addition and multiplication as you'd expect. In some sense, the ring structure of this set is at the heart of why every integer can be written as a sum of four squares.
 September 2nd, 2017, 04:26 AM #4 Senior Member   Joined: Nov 2011 Posts: 175 Thanks: 2 cool
 September 2nd, 2017, 04:28 AM #5 Senior Member   Joined: Nov 2011 Posts: 175 Thanks: 2 other thing How can I design the message in Real English. If somebody help I will be happy. other question: what is mean of "quaternion units."?! I need little explainsion, or example or something else. Last edited by shaharhada; September 2nd, 2017 at 04:47 AM.
 September 2nd, 2017, 05:05 AM #6 Global Moderator   Joined: Dec 2006 Posts: 18,594 Thanks: 1492 Your English is quite good, and better than that of some people who have English as their main language.
 September 2nd, 2017, 05:25 AM #7 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,959 Thanks: 801 Google "Quaternion". In particular look at https://en.wikipedia.org/wiki/Quater...atial_rotation.

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