Answer to Question #106140 in Complex Analysis for khushi

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=\\sqrt[6]{-7}\\\\\nz^6=-7\\\\\nz^6=7e^{\\pi i}\\\\\nz^6=7e^{(2\\pi n+\\pi) i} \\quad\\quad n=0,1,...5\\\\\nz=7^{\\frac{1}{6}} e^{\\frac{2\\pi n+\\pi}{6} i} \\quad\\quad n=0,1,...5\\\\\nz=1.383e^{(\\frac{\\pi n}{3}+\\frac{\\pi}{6}) i} \\quad\\quad n=0,1,...5"


six answers are,

"z_1=1.383e^{\\frac{\\pi}{6} i} \\\\\nz_2=1.383e^{\\frac{\\pi}{2} i} =1.383i\\\\\nz_3=1.383e^{\\frac{5\\pi}{6} i} \\\\\nz_4=1.383e^{\\frac{7\\pi}{6} i} \\\\\nz_5=1.383e^{\\frac{3\\pi}{2} i} =-1.383i\\\\\nz_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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