4. Simplify the following expressions and express the results in rectangular form. Use at least 5-significant digits (s.d.) in your calculations and use 4-s.d. in your answer. (a) (b) (c) (5-j6) (2 + j8) (−3+ j4)(5−j) + (4 – j6) (240/75°+ 160/-30°)(60- j80) (67+j84)(20/32°) 3+40) √(10 + j5)(16-j20)

Problem 1 Perform the following mathematical operations with complex numbers, and express your answer in polar and rectangular form: (0.4 2-60°)(3004-70") d) 3-j9

Activity 1: You are testing an electrical device which can be modelled by the figure shown below: 18 -j12 a b j6 -j10 it E1 12 13 E2 13 The above electric circuit can be characterized by the following equations: 1811 + j6(11 – 12) + 4(11 – 12) = 1020° -j1212 + 8(12 – I3) + 20490° + 4(I2 – 4) + j6(I2 – I1) = 0 -j1013 + 1313 – 20290° + 8(13 – 12) = 0 Find I1, I2, and I3 using the Gaussian elimination method.

When the switch is in position 2, the circuit will discharge the capacitor. Draw the circuit for the discharge phase. (without any of the charge phase components). and determine the time constant for the discharge phase and the equations for v(t) and i(t) for the discharge phase.