Quaternion Calculator
MathPerform sum, difference, product, conjugate, or magnitude operations on quaternions, four-dimensional numbers extending complex numbers.
Result: real part
For sum/difference/product, the real part of the resulting quaternion. For conjugate, the unchanged real part. For magnitude, the full result (the other three outputs are not used).
Result: i coefficient
-10.000000
The i coefficient of the result (sign-flipped for conjugate).
Result: j coefficient
12.000000
The j coefficient of the result (sign-flipped for conjugate).
Result: k coefficient
19.000000
The k coefficient of the result (sign-flipped for conjugate).
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Odeh Ahwal0people find this calculator helpful
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Calculator Stats
Creators
Odeh Ahwal0people find this calculator helpful
Views
Helpful
Saved
Embeds
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Frequently Asked Questions
What is a quaternion?
A quaternion extends complex numbers into four dimensions, written as a + bi + cj + dk, where i, j, and k are three different imaginary units that each square to -1, with their own multiplication rules between them.
What are quaternions used for?
They are widely used to represent 3D rotations in computer graphics, robotics, and aerospace, since they avoid a problem called gimbal lock that affects other rotation representations.
Which quaternion operations does this calculator skip?
Quotient, inverse, and quaternion-of-rotation are not included here, only the more fundamental sum, difference, product, conjugate, and magnitude operations. Those three more advanced operations are meaningful extensions but were left out of this version's scope.
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