+0

0
124
2

What are the 3 roots of this expression?
∛-512² . Thank you for help.

Apr 8, 2019

#2
+1

Maybe:

∛-512² = 64
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = -8
Power: (-8) ^ 2 = 64

∛-512² = -32-55.4256258i = 64 × ei (-120°)
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = 4-6.9282032i
Power: (4-6.9282032i) ^ 2 = (4-6.9282032i) * (4-6.9282032i) = 16-27.712812i-27.712812i-47.999997 = -32-55.4256258i

∛-512² = -32+55.4256258i = 64 × ei 120°
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = 4+6.9282032i
Power: (4+6.9282032i) ^ 2 = (4+6.9282032i) * (4+6.9282032i) = 16+27.712812i+27.712812i-47.999997 = -32+55.4256258i

Apr 8, 2019

#2
+1

Maybe:

∛-512² = 64
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = -8
Power: (-8) ^ 2 = 64

∛-512² = -32-55.4256258i = 64 × ei (-120°)
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = 4-6.9282032i
Power: (4-6.9282032i) ^ 2 = (4-6.9282032i) * (4-6.9282032i) = 16-27.712812i-27.712812i-47.999997 = -32-55.4256258i

∛-512² = -32+55.4256258i = 64 × ei 120°
Divide: 1 / 3 = 0.33333333
Power: (-512) ^ 0.3333333 = -512 ^ 0.3333333 = 4+6.9282032i
Power: (4+6.9282032i) ^ 2 = (4+6.9282032i) * (4+6.9282032i) = 16+27.712812i+27.712812i-47.999997 = -32+55.4256258i

Guest Apr 8, 2019