We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
59
2
avatar

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

 Apr 8, 2019

Best Answer 

 #2
avatar
+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
avatar
+1
Best Answer

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

17 Online Users