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Q1. (a) Given Z₁ = 3a + j5a and Z₂ = 11b + j2b. Solve the follow complex equation for a and b, where a and b are real numbers: Z₁ + Z₂ = - 7 + j21 (8)

(b) Three mooring lines exert horizontal forces on a bollard, positioned at O, as follows:

20 kN at 30°

16 kN at 70°

10 kN at 85°

The angles are those that the forces make with the real axis Ox.

Determine using complex numbers the magnitude and direction of the resultant force on the bollard. (8)