assgt2 - B is a complex number. (i) ( 8 marks ) Show that |...

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MATH 407-10a, Assignment 2 Guidelines Answer the questions in the space provided; you may write on both sides of the paper. Put the names of all group members in the top right corner. You may append additional sheets as needed. Please staple all sheets together before submission. Due: Thursday, Jan 28th (in class) 1. Suppose that A is a real number and
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Unformatted text preview: B is a complex number. (i) ( 8 marks ) Show that | z + A | 2-2Re( Az ) = | z | 2 + A 2 . (ii) ( 8 marks ) Shew that | z + B | 2- | B | 2 = | z | 2 + 2Re( Bz ) . 2. ( 9 marks ) Let be a complex number with modulus 1. Prove that Arg -1 + 1 = / 2 , if Im( ) > 0;-/ 2 , if Im( ) < 0....
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