Unformatted text preview: w = n √ r [cos (θ/ n ) + i sin (θ/ n ) ] is an n th root of z , where r ≥ 0. Solution. By De Moivre ’ s theorem, w n = ( n √ r ) n ( [cos (θ/ n ) + i sin (θ/ n ) ] ) n = r [ cos (θ) + i sin (θ) ] . (ii) Show that every n th root of z has the form ζ k w , where ζ is a primitive n th root of unity and k = , 1 , 2 , . . . , n − 1....
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.
- Fall '11