To find one of the values of (−64i)5∕6, let's proceed with the computation: Let Z=(−64i)5∕6. We can express Z as: Z=((−i)5)1∕6×(64)5∕6 Calculate (64)5∕6 : 645∕6=32 Handle the imaginary unit: Since (−i)5=−i, we represent this in polar coordinates: −i=cos(‌
3Ï€
2
)+isin‌(‌
3Ï€
2
) Find (−i)1∕6 : Using De Moivre's theorem, (−i)1∕6 can be expressed as: ‌(−i)1∕6=[cos(‌
3Ï€
2
)+isin‌(‌
3Ï€
2
)]1∕6 ‌=cos(‌
3Ï€
12
)+isin‌(‌
3Ï€
12
) ‌=‌
1
√2
(1+i) Combine the results: Therefore, Z becomes: Z=32×‌
1
√2
(1+i)=16√2(1+i) The calculation yields one of the values of (−64i)5∕6 as 16√2(1+i).