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Unformatted text preview: < e stands for “real” part of a complex number) 1 5. (10 Points) Determine real and imaginary parts of following complex number: (1 + j )2011 (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. (30 Points) By use of Euler’s formula show that: (a) cos θ = 1θ 2 2! + θ 4 4!θ 6 6! +            ∞ sin θ = θθ 3 3! + θ 5 3!θ 7 7! +            ∞ (b) 1 . Z e aθ sin bθ · dθ = e aθ a 2 + b 2 · ( a sin bθb cos bθ ) 2 . Z e aθ cos bθ · dθ = e aθ a 2 + b 2 · ( a cos bθ + b sin bθ ) (c) cos( A + B ) = cos A · cos Bsin A · sin B (Hint: e jθ = cos θ + j sin θ ) 2...
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 Spring '08
 SHIN
 Sin, Cos, Complex number, following equation, imaginary parts, Reviews of Complex Number

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