1. Quaternion Arithmetic Elmer Nocon Angelo Bernabe Mark Hitosis

2. Quaternion Addition Let and be two quaternions. the sum of P and Q is

3. Quaternion Addition Let and be two quaternions. the sum of P and Q is

4. Quaternion Addition Let and be two quaternions. the sum of P and Q is e5

5. Quaternion Addition Let and be two quaternions. the sum of P and Q is

6. Quaternion Addition Let and be two quaternions. the sum of P and Q is e

7. Quaternion Addition Example: Let and be two quaternions. the sum of S and T is

8. Quaternion Subtraction Let and be two quaternions. the difference of P and Q is

9. Quaternion Subtraction Let and be two quaternions. the difference of P and Q is

10. Quaternion Subtraction Let and be two quaternions. the difference of P and Q is

11. Quaternion Subtraction Let and be two quaternions. the difference of P and Q is

12. Quaternion Subtraction Let and be two quaternions. the difference of P and Q is

13. Quaternion Subtraction Example: Let and be two quaternions. the difference of S and T is

14. Quaternion Multiplication Let and be two quaternions. the product of P and Q is

15. Quaternion Multiplication Let and be two quaternions. the product of P and Q is we distribute

16. When we multiply the imaginary operators we use the following rules:

17. When we multiply the imaginary operators we use the following rules:

18. When we multiply the imaginary operators we use the following rules:

19. then we simplify our newly derived formula

20. Quaternion Multiplication Example: Let and be two quaternions. the product of S and T is using our formula

21. Quaternion Division Let and be two quaternions. to find the quotient of P and Q we need to multiply P by the reciprocal of Q and to find the Q-1, we need to find the conjugate of q and divide it by the normal of q

22. Quaternion Conjugation Let be a quaternion. the conjugate of P is

23. Quaternion Conjugation Example: Let be a quaternion. the conjugate of P is

24. Normal of a Quaternion Let be a quaternion. the normal of P is

25. Normal of a Quaternion Example: Let be a quaternion. the normal of P is

26. Reciprocal of a Quaternion Let be a quaternion. the reciprocal of P is

27. Reciprocal of a Quaternion Example: Let be a quaternion. the reciprocal of P is

28. Quaternion Division Example: Let and be two quaternions. the quotient of P and Q is

29. Quaternion Division we use our formula in quaternion multiplication