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anonymous
 5 years ago
given z^6=1, find all complex solutions for z. Can anyone guide me through the steps required to solve this?
anonymous
 5 years ago
given z^6=1, find all complex solutions for z. Can anyone guide me through the steps required to solve this?

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nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Use polar coordinates for z, \[z = re^{iφ}\] then set radius and arcs equal, but observe periodicity.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This can be written as z^6  1 = 0 then z^6  1^6 = 0 Continue with sum and difference of cubes formula: (z^3 + 1)(z^3  1) = 0 (z + 1)(z^2  z + 1)(z  1)(z^2 + z + 1) = 0 This yields z = ±1 and z = (±1 ± i√3)/2. That's all 6.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hope this helps, I have time constraint or would hv gone into details
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