hw1 - 1 Home Work 1. Two pages. Reading assignments dont...

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1 Home Work 1. Two pages. Reading assignments don’t have to be turned in. You can choose to do the problems in this homework or the exercises in sections 2.1–2.5 of my notes posted on the class web-site. 1. Reading assignment. Read chapter 2 of the notes posted on the class web-site. 2. Find a way to represent complex numbers as 2 × 2 real matrices, such that arithmetic operations (+, , × , and ÷ ) on complex numbers becomes equivalent to arithmetic operations on their matrix representations instead. That is, if T ( z ) is the 2 × 2 real matrix representing the complex number z , then T ( z 1 + z 2 ) = T ( z 1 ) + T ( z 2 ) , T ( z 1 z 2 ) = T ( z 1 ) T ( z 2 ) , T ( z 1 z 2 ) = T ( z 1 ) T ( z 2 ) , T ( z 1 /z 2 ) = ( T ( z 2 )) 1 T ( z 1 ) , for all complex numbers z 1 and z 2 . Hint: The entries of T ( z ) will depend on the real and imaginary parts of z . Look at the expression for the product of two complex numbers and two 2 × 2 matrices. 3. A. Show that the
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This note was uploaded on 10/13/2010 for the course ECE ECe210a taught by Professor Chandrashekharan during the Fall '10 term at UCSB.

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hw1 - 1 Home Work 1. Two pages. Reading assignments dont...

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