Elements in sets that are common

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SUMMARY

The discussion focuses on finding the intersection of sets A, B, and C, where A consists of the roots of the equation z6 = √3 + i, B includes complex numbers with a positive imaginary part, and C includes those with a positive real part. The roots of z6 are derived from the polar form of the complex number, and the task is to identify which of these roots satisfy the conditions of being in both B and C. The solution involves determining the real and imaginary parts of the roots and confirming their positivity.

PREREQUISITES
  • Understanding of complex numbers and their polar representation
  • Knowledge of the roots of unity and De Moivre's Theorem
  • Familiarity with the concepts of real and imaginary parts of complex numbers
  • Basic skills in visualizing complex planes and unit circles
NEXT STEPS
  • Study the roots of unity and their geometric interpretations
  • Learn about De Moivre's Theorem for calculating powers and roots of complex numbers
  • Explore the properties of complex numbers in the Argand plane
  • Investigate the conditions for complex numbers to lie in specific quadrants
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Mathematics students, particularly those studying complex analysis, and anyone interested in solving polynomial equations involving complex numbers.

ronho1234
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let A={z|z^6=√3 + i} B=(z|Im(z)>0} and C={z|Re(z)>0} find A∩B∩C
the part previous to this qn asks me to find the roots of z^6 and I've already down that. but i have no idea how to proceed with this, so do i draw my unit ciorcle with the hexagon and then follow to see what regions satisfies with the other 2? please help
 
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Can you show the roots of z^6=sqrt(3)+i? Because if you write them down you just need to decide which ones have Real part positive AND have imaginary part positive. That should not be too hard as w=a+bi has Re(w)>0 iff a>0 and Im(w)>0 iff b>0
 

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