This preview shows page 1. Sign up to view the full content.
Unformatted text preview: + j sin k N , expressing your answer in Cartesian form. (Use the identity 1+2+ + n = n ( n +1) / 2 to simplify the answer rst.) S 2.2 . Show that the expression f ( ) = e-j 2 -e-j + 1-e j + e j 2 , where ranges over [0 , 2 ), is real-valued, and obtain an alternative expression for it in terms of sines and/or cosines. S 2.3 . Clearly, e j 3 = e j 3 By expanding (cos + j sin ) 3 and separating real and imaginary parts, obtain two identities: one for cos3 in terms of powers of cos only, and another for sin3 in terms of powers of sin only. S 2.4 (more dicult). Consider two complex numbers w and z , where w 6 = 0 is xed and z is variable such that | z | = 1. Show that as z traces out the unit circle, the ratio | z-w * | | z-(1 /w ) | is constant in value. ( Hint : If | z | = 1, then 1 /z = z * .)...
View Full Document
This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08