extra_1 - Extra Problems Sheet 1 Stephen Taylor 1 Consider...

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Unformatted text preview: Extra Problems Sheet 1 Stephen Taylor April 28, 2005 1. Consider the complex number z = √ 3+5 i 6- 4 √ 3 i (a) Write z in the standard form x + iy √ 3 + 5 i 6- 4 √ 3 i · 6 + 4 √ 3 i 6 + 4 √ 3 i =- 14 √ 3 + 42 i 84 =- √ 3 6 + i 2 (b) Find the conjugate of z ¯ z =- √ 3 6- i 2 (c) Find the modulus of z | z | = s √ 3 6 2 + 1 2 2 = √ 3 3 (d) Find the argument of z arg z = arctan- 1 2 · 6 √ 3 = arctan(- √ 3) =- π 3 (e) Write z in polar form z = √ 3 3 e- i π 3 2. Given the arbitrary complex numbers, z , shown in the graph below, represent each of the following on the given separate graphs. 1 (a) ¯ z Figure 1 z s (b) z + (1- i ) Figure 2 z s (c) z 2 Figure 3 z s (d) z ¯ z 2 Figure 4 z s (e) z- 1 Figure 5 z s 3. Describe the set of points z in the complex plane that satisfy each of the following: (a) | z- i | < 2 This set is an open disk of radius 2 centered at (0 , i )....
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This note was uploaded on 10/19/2009 for the course MATH 814 taught by Professor Cong during the Three '09 term at University of Adelaide.

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extra_1 - Extra Problems Sheet 1 Stephen Taylor 1 Consider...

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