Question #110806
Obtain the 6th roots of (-7) , and represent them in an Argand diagram
1
Expert's answer
2020-04-20T17:30:40-0400

z=(7)1/6z=(-7)^{1/6}

z6=7z^6=-7

z6=7eπiz^6=7e^{πi}

z6=7e2πn+πiz^6=7e^{2πn+πi}

z=71/6e2πn+πi6z=7^{1/6}e^{\frac{2πn+πi}{6}}

z1=71/6eπ6iz_1=7^{1/6}e^{\frac{π}{6}i}

z2=71/6eπ2iz_2=7^{1/6}e^{\frac{π}{2}i}

z3=71/6e5π6iz_3=7^{1/6}e^{\frac{5π}{6}i}

z4=71/6e7π6iz_4=7^{1/6}e^{\frac{7π}{6}i}

z5=71/6e3π2iz_5=7^{1/6}e^{\frac{3π}{2}i}

z6=71/6e11π6iz_6=7^{1/6}e^{\frac{11π}{6}i}


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