# Complex Numbers

See the attached file.

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

n

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

z2

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.

https://brainmass.com/math/complex-analysis/logarithm-complex-numbers-93317

#### Solution Summary

Logarithm and complex numbers problems are solved.