ENEE241hw01

# ENEE241hw01 - ENEE 241 02 HOMEWORK ASSIGNMENT 1 Due Tue...

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ENEE 241 02 HOMEWORK ASSIGNMENT 1 Due Tue 02/08 Problem 1A Consider the complex numbers z 1 =2 3 j and z 2 = 1+8 j (i) (2 pts.) Plot both numbers on the complex plane. (ii) (2 pts.) Evaluate | z i | and ° z i for both values of i ( i =1 , 2). (iii) (4 pts.) Express each of 2 z 1 z 2 and z 1 /z 2 in both Cartesian and polar form. (iv) (3 pts.) If v = z 1 · z 3 2 ,determ ine | v | and ° v . Also, obtain v in Cartesian form. (v) (3 pts.) If w = z 4000 1 ,de term ine ° w in the range [0 , 2 π ). Your answer should be correct to Fve decimal places. (vi) (3 pts.) Determine the only real values of a and b such that z 2 + az + b =0 has z =2 z 1 z 2 as a root. (vii) (3 pts.) Without using a calculator, show that ° z 1 and ° ( z 1 + z 2 ) di±er by an integer multiple of π/ 4. ( Hint: Use coordinate geometry; specifcally, the dot product between two vectors. ) Problem 1B Do not use a calculator For this problem. Express your answers using square roots and/or Fractional

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## This note was uploaded on 09/27/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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ENEE241hw01 - ENEE 241 02 HOMEWORK ASSIGNMENT 1 Due Tue...

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