An insect starts from the origin in the argand plane and goes 4   k m ( N   45 °   E ) then it moves 3   k m   N   45 ° W and then takes an angular movement of π 3 about origin in the anticlockwise direction. The final position of the insect is

Step-by-step solution

Travelling 4   k m   N   45 ° E it reaches at z 1 = 4 e i π 4 Travelling 3   k m   N   45 ° W it reaches at z 2 So, 0 - z 1 z 2 - z 1 = 4 3 i ⇒ z 2 = 4 + 3 i e i π 4 After an angular movement of π 3 in the anticlockwise direction it reaches at z 3 ∴ z 3 = z 2 e i π 3 = 4 + 3 i e i 7 π 12