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What are the fourth roots of 2√3−2i ? Enter the roots in order of increasing angle measure.

 

___cis(___)

 

___cis(___)

 

___cis(___)

 

___cis(___)

 Aug 25, 2021
 #1
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first convert to polar form

\(2\sqrt{3}-2i\\=4(\frac{\sqrt{3}}{2}-\frac{i}{2})\\=4(\cos(-30)+i\sin(-30))\\=4(cis(-30))\)

The magnitude will be fourth-rooted, while the angle will divide by 4. 

Also, note that adding 90 to the angle will still make it a root, because 90*4=360.

Therefore the answers are:

\(\sqrt{2}(cis(-7.5)), \sqrt{2}(cis(-7.5)+90), \sqrt{2}(cis(-7.5+180)), \sqrt{2}(cis(-7.5+270))\)

 Aug 25, 2021

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