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 ² z1 z + 1 ³ = ´ π/ 2 , if Im( z ) > 0;π/ 2 , if Im( z ) < 0. 10. Show that De Moivre’s 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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 Fall '08
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 Complex Numbers, 1 K, Complex number, de Moivre

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