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Unformatted text preview: Solve the following equation for a complex variable z : z 4 =j (Be sure to ﬁnd all possible answers, and express your answers in polar form and plot all the solutions on the complex plane with magnitude and angle) 5. (20 Points) Evaluate following complex number: (1 + j ) 2007 (Hint: Use following formula and polar form representation of the complex number, i.e., 1 √ 2 (1 + j ) = e jπ/ 4 ) (cos θ + j sin θ ) n = cos nθ + j sin nθ 6. (20 Points) By use of Euler’s formula show that: Z e ax sin bxdx = 1 a 2 + b 2 · e ax · ( a sin bxb cos bx ) Z e ax cos bxdx = 1 a 2 + b 2 · e ax · ( a cos bx + b sin bx ) 2...
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 Spring '08
 J.Shin
 Digital Signal Processing, Signal Processing, Complex number, Euler's formula, Reviews of Complex Number, b2 eax sin

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