Question: how to do this question 3. (10 points) Suppose a complex number z satisfies the equation 272 - (3+81)z - (m+ 41) = 0. Given

how to do this question

how to do this question 3. (10 points) Suppose a complex number

3. (10 points) Suppose a complex number z satisfies the equation 272 - (3+81)z - (m+ 41) = 0. Given that m is a real constant and that one of the two solutions is real, find the two solutions of the above complex quadratic equation. (Hint: The real solution is easy to find. To find the other solution, use the fact that the two solutions z1, Z2 of the quadratic equation azz + bz + c = 0 satisfy z1 + z2 = -b/a.) 4. (15 points) Find all the complex solutions of the equation z* + (V3 -31)(1+z)4 = 0. Express the results in Cartesian form (you may express your answer as a function of k, e.g. z = el(kn/2) = + cos(kn /2) + isin(kit/2), k = 0, 1,2, 3, without explicitly evaluating the expression for each k)

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