Quaternions

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/Med/fag here, can someone explain me quaternions? Is it possible to explain it logically in a simple way?
My math knowledge is basic, my Complex number is basic as well
How is it possible that {\displaystyle \mathbf {i} ^{2}=\mathbf {j} ^{2}=\mathbf {k} ^{2}=\mathbf {ijk} =-1.} ? Can you explain me?