homework1 - re i a ) i-2-2 i ; b ) ( 3-i ) 4 ; c ) (1-i ) 5...

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Due 01-16-09 Physics 132 Winter 2009 P. Kraus HOMEWORK #1 Hand into box marked “132” outside 1-707D PAB by 3pm Fri. —————————————————————————————————————————— 1) BC p. 5 (1a) and (1b). Verify: a ) ( 2 - i ) - i (1 - 2 i ) = - 2 i ; b ) (2 , - 3)( - 2 , 1) = ( - 1 , 8) 2) Write each of the following complex numbers in the form x + iy a ) (1 + 3 i ) 3 ; b ) (1 + i ) 2 (1 - i ) ; c ) (1 + i 3) 3 (1 - i ) 2 3) BC p. 12 problem 4: Verify that 2 | z | ≥ | Re z | + | Imz | 4) BC p. 5 problem 5: In each case, sketch the set of points determined by the given condition: a ) | z - i + i | = 1 ; b ) | z + i | ≤ 3 ; c ) | z - 4 i | ≥ 4 5) Write each of the following complex numbers in the form
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Unformatted text preview: re i a ) i-2-2 i ; b ) ( 3-i ) 4 ; c ) (1-i ) 5 6) BC p. 23 problems (5a) and (5d): By writing the individual factors on the left in exponential form, performing the needed operations, and nally changing back to rectangular coordinates, show that a ) i (1- 3 i )( 3 + i ) = 2(1 + 3 i ) ; d ) (1 + 3 i )-10 = 2-11 (-1 + 3 i ) 7) Find all values of the following roots and write them in the form x + iy a ) (-1) 1 / 3 ; b ) 8 1 / 6 1...
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