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In a R-C series circuit shown in figure 2
1 a) In a R-C series circuit shown in figure 2, V. lags 1 by 90° and may be written as VR-jV₂ = V, from which R-jX = Z, where X is the capacitive reactence) and X = 2ПfC с R HH VA Vc V Figure 2:R-C circuit You are asked to deteremine the resistance and series capacitance for each of the following impendances Z₁ and Z₂ assuming a frequency of 50Hz. i) 2 - 3j ii) 4 -5j b) i) Express Z₁ and Z₂ in polar form and exponential form. ii) Find Z₁ Z₂ and in polar form and exponential form. iii) Deduce Z₁² using De Moivre's theorem. iv) Show that sin30 = 3sin0 - 4sin³0 using De Moivre's theorem.