Answer Happy

Application of voltage division with phasor format
Can't figure out what I've highlighted in blue. How to do basic
multiplication of a fraction when there is j and phasor format to
get the answer of -64 + j 32 V.
Thank you!
a) Section II: computation questions Question 4 12 Marks Given the following AC circuits as shown in (a), v₂ (t) = 80 cos (100t) volts, R=502, C=50 μF, L=1 H, use phasors to do the following: a) Find the Thevenin equivalent circuit with respect to terminals A-B; (8 marks) b) For the given frequency of operation, draw the Thevenin equivalent circuit in terms of a time varying voltage source with a resistor and an inductor or capacitor (specify the value of the resistance and capacitance/inductance); (2 marks) c) For the circuit as shown in (b), find what type of circuit element must be in the box to make the Thevenin equivalent impedance seen at terminals C-D be purely resistive, and what would be the value X of that element? (2 marks) R с R ww A A ww C mga v₁ (t) LVth v₁(t) (a) (b) Vict) = 80 cos (100 €) → √₁ = 80 Dº ZR = 5052 Z₁ = 1/jwc = 1/√ × 100×50×100 = -1200 52 Z = jwL = jx100x1 = j100 52 By applying voltage divider : jcoo Ze -641 32 V Vi. ・8060⁰x jioo 1200 +50 j = + Ec+ ZR 11=₁ (64)³²+32²2² = 71.56 V argiven ] = arc tan (²4) = −26.57°±n•180°, n= 0₁1₁2--- • √th = -64+3 32 is in the 2nd quadrant, I COCT :. arg {vin f = −2657° + 180° = 153. 43° • Vtn = -64 +ĵ32 = 71.56 /153.43° V =th = {ZR + Zc ) " Z₁ = [50-Ĵ200311 Ĵ100 = 40+j18052 = B OD