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Q1) a) Solve the following complex equation for a and b, where a and b are real numbers:

(3 + ja)/(3 + jb) = (2a + b)/(2b + j3) (8)

(b) Two impedances, Z₁ = 3 + j8 and Z₂ = 5 - j4 are connected in series to a supply voltage, v, of 250 volts.

Calculate the current, i amperes, as a complex number in polar form, given that

i = v/Z where Z = Z₁ + Z₂. (8)