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Q1) (a) THREE mooring lines exert horizontal forces on a bollard, positioned at O, as follows:

18 kN at 55°

35 kN at 85°

42 kN at 140°

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)

(b) Given Z₁ = 2a + j7a and Z₂ = 9b + j5b, solve the following complex equation for a and b, where a and b are real numbers:

Z₁ + Z₂ = 30 - j. (8)