Hello, I'm having trouble with finding the three cube roots of z=125cis48°. Can anyone explain the steps? My test is next week. :[
Any help is appreciated. :]
Any help is appreciated. :]
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By applying DeMovire's Theorem:
(125 cis 48°)^(1/3) = 125^(1/3) * cis[(48° + 360°k)/3], for k = 0, 1, and 2
= 5cis(16° + 120°k).
Therefore, by letting k = 0, 1, and 2:
(i) k = 0 ==> (125 cis 48°)^(1/3) = 5cis(16°)
(ii) k = 1 ==> (125 cis 48°)^(1/3) = 5cis(136°)
(iii) k = 2 ==> (125 cis 48°)^(1/3) = 5cis(256°).
I hope this helps!
(125 cis 48°)^(1/3) = 125^(1/3) * cis[(48° + 360°k)/3], for k = 0, 1, and 2
= 5cis(16° + 120°k).
Therefore, by letting k = 0, 1, and 2:
(i) k = 0 ==> (125 cis 48°)^(1/3) = 5cis(16°)
(ii) k = 1 ==> (125 cis 48°)^(1/3) = 5cis(136°)
(iii) k = 2 ==> (125 cis 48°)^(1/3) = 5cis(256°).
I hope this helps!