If z 1 , z 2 and z 3 are 3 distinct complex numbers such that 3 z 1 - z 2 = 5 z 2 - z 3 = 7 z 3 - z 1 , then the value of 9 z 1 - z 2 + 25 z 2 - z 3 + 49 z 3 - z 1 is equal to

Step-by-step solution

Let, 3 z 1 - z 2 = 5 z 2 - z 3 = 7 z 3 - z 1 = k 9 z 1 - z 2 2 = 25 z 2 - z 3 2 = 49 z 3 - z 1 2 = k 2 ⇒ 9 z 1 - z 2 z - 1 - z - 2 = k 2 ⇒ 9 z 1 - z 2 = k 2 z - 1 - z - 2 similarly, 25 z 2 - z 3 = k 2 z - 2 - z - 3 and 49 z 3 - z 1 = k 2 z - 3 - z - 1 ⇒ 9 z 1 - z 2 + 25 z 2 - z 3 + 49 z 3 - z 1 = k 2 z - 1 - z - 2 + z - 2 - z - 3 + z - 3 - z - 1 = 0