Question #106140
Obtain the 6th roots of (−7) , and represent them in an Argand diagram.
1
Expert's answer
2020-03-21T12:33:53-0400

z=76z6=7z6=7eπiz6=7e(2πn+π)in=0,1,...5z=716e2πn+π6in=0,1,...5z=1.383e(πn3+π6)in=0,1,...5z=\sqrt[6]{-7}\\ z^6=-7\\ z^6=7e^{\pi i}\\ z^6=7e^{(2\pi n+\pi) i} \quad\quad n=0,1,...5\\ z=7^{\frac{1}{6}} e^{\frac{2\pi n+\pi}{6} i} \quad\quad n=0,1,...5\\ z=1.383e^{(\frac{\pi n}{3}+\frac{\pi}{6}) i} \quad\quad n=0,1,...5


six answers are,

z1=1.383eπ6iz2=1.383eπ2i=1.383iz3=1.383e5π6iz4=1.383e7π6iz5=1.383e3π2i=1.383iz6=1.383e11π6iz_1=1.383e^{\frac{\pi}{6} i} \\ z_2=1.383e^{\frac{\pi}{2} i} =1.383i\\ z_3=1.383e^{\frac{5\pi}{6} i} \\ z_4=1.383e^{\frac{7\pi}{6} i} \\ z_5=1.383e^{\frac{3\pi}{2} i} =-1.383i\\ z_6=1.383e^{\frac{11\pi}{6} i}

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Comments

Assignment Expert
23.10.20, 19:52

Dear Shubham, please use the panel for submitting new questions.

Shubham
23.10.20, 17:41

Give another way for this answer using de moivre's theorem

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