ABSTRACT
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)
