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Unformatted text preview: z with itself). 7. Suppose n is a positive integer and a ,...,a n are real numbers. Let P ( z ) := n k =0 a k z k , z C (where z := 1). Prove that P ( z ) = 0 for some complex number z if and only if P ( z ) = 0. 8. Give an example to show that Arg( zw ) need not equal Arg( z ) + Arg( w ). 9. Suppose | z | = 1. Show that Arg z-1 z + 1 = / 2 , if Im( z ) > 0;-/ 2 , if Im( z ) < 0. 10. Show that De Moivres formula holds for negative integers n as well. 11. Suppose z = x + iy is a complex number. Prove that | z | | x | + | y | 2 | z | . 1...
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This note was uploaded on 03/08/2010 for the course MATH 407 taught by Professor Staff during the Fall '08 term at Texas A&M.
- Fall '08
- Complex Numbers