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    Complex Numbers

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    1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56.

    2. Solve log(2x + 3) = log(4x) + 2, for x giving the answer correct to 3 significant figures.

    3. For a thermodynamic process involving a perfect gas, the initial and final temperatures are related by:

    T1 exp(^s/Cp) = T2

    Where Cp is the specific heat capacity of the gas, ^s is the change of entropy and T1 and T2 are the initial and final temperatures of the process. Determine the value of ^s (units - kJ/kg) if T1 = 320 K, T2 = 450K and Cp = 1.005 kJ/kg K.

    4.Transform the formula
    Y1 = X1
    Y2 X2

    To make n the subject.

    5. Make y the subject of the formula:
    E = P(1 - e(y - 1))

    6. Given the complex numbers:

    z1 = 5 - j4 z2 = 4 + j z3 = -6 - j7 z4 = j2

    Calculate, giving answers in the form a +jb, the following:

    (i) z4 - z1 + z2
    (ii) 3z1 - 2z3 + z4
    (iii) z1z2
    (iv) z3

    7. Simplify each of the following giving your answer as a complex number in polar form:

    (i) 12 / 40degrees * /135degrees

    (ii) 32 /-15 degrees
    8 / 48degrees.

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    Solution Summary

    Logarithm and complex numbers problems are solved.