Question: Let w be a negative real number, z a 6th root of w. (a) Show that z (k) = ^(1/6) cos ((+2k)/ 6) + isin

Let w be a negative real number, z a 6th root of w.

(a) Show that z (k) = ^(1/6) cos ((+2k)/ 6) + isin ((+2k)/ 6), k = 0, 1, 2, 3, 4, 5 is a formula for the 6th roots of w.

(b) Hence determine the 6th roots of 729.

(c) Given z = cos + isin and u + iv = (1 + z)(1 + z^2 ). Prove that v = u tan((3)/2 ) and u^2 + v^2 = 16 cos^2 ( /2 ) cos^2 ()

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