Z2 = (3 − j4) ohms, are connected in series to a supply voltage V of 150∠0◦ V. Determine the magnitude of the current I and its phase angle relative to the voltage. (6)

5. Determine in both polar and rectangular forms:

(a) [2.37∠35◦]4 (b) [3.2 − j4.8]5 (c) √[−1 − j3] (15)

In questions 6 to 10, the matrices stated are:

A = (−5 2

7 −8 )

B = ( 1 6 −3 −4

)

C = (j3 (1 + j2)

(−1 − j4) −j2 )

D = ⎛

⎝ 2 −1 3

−5 1 0 4 −6 2

⎞

⎠ E = ⎛

⎝ −1 3 0

4 −9 2 −5 7 1

⎞

⎠

6. Determine A × B (4) 7. Calculate the determinant of matrix C (4) 8. Determine the inverse of matrix A (4) 9. Determine E × D (9)

10. Calculate the determinant of matrix D (6) 11. Solve the following simultaneous equations:

4x − 3y = 17 x + y + 1 = 0

using matrices. (6) 12. Use determinants to solve the following simul-

taneous equations: 4x + 9y + 2z = 21

−8x + 6y − 3z = 41 3x + y − 5z = −73 (10)

13. The simultaneous equations representing the currents flowing in an unbalanced, three-phase, star-connected, electrical network are as follows:

2.4I1 + 3.6I2 + 4.8I3 = 1.2 −3.9I1 + 1.3I2 − 6.5I3 = 2.6 1.7I1 + 11.9I2 + 8.5I3 = 0

Using matrices, solve the equations for I1, I2 and I3 (10)