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Complex numbers › The complex plane › Extremes of the modulus

Maximum modified distance between unit quaternions

University · ●●○○○ 20 pts

For unit quaternions q1q_1 and q2q_2 (so ∥q1∥=∥q2∥=1\|q_1\|=\|q_2\|=1), define d(q1,q2)=2min⁡(∥q1−q2∥,∥q1+q2∥)d(q_1,q_2)=2\min(\|q_1-q_2\|,\|q_1+q_2\|). Find the maximum value of d(q1,q2)d(q_1,q_2). Round to two decimal places.

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euclidean distanceoptimization