Question: Consider the polynomial equation z^5 = 243. (a)How many solutions does this equation have when z R? How many solutions do it have when z

Consider the polynomial equation

z^5 = 243.

  1. (a)How many solutions does this equation have when z R? How many solutions do it have when z C? Give a brief explanation of why these numbers are the same or why they are different.
  2. (b)Find all solutions to this equation when z C and show that solutions with an imaginary part occur in complex conjugate pairs.

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