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Let A z 1 , B z 2 and C ( z 3 ) be complex numbers satisfying the equation z = 1 and also satisfying the relation 3 z 1 = 2 z 2 + 2 z 3 . Then z 2 - z 3 2 is equal to

Correct answer

1.75

Step-by-step solution

A , B , C lie on the unit circle centered at the origin. Also, 3 z 1 + 1.0 4 = z 2 + z 3 2 i.e. the line segment joining z 1 and origin D bisects the line segment joining z 2   &   z 3 at E Also, D E : E A ≡ 3 : 1 Let D E = 3 K and E A = K Now, D A = 4 K = 1 ⇒ K = 1 4 ⇒ D E = 3 4 From △ B E D , BE = 1 - 9 16 = 7 4 ⇒ z 2 - z 3 = B C = 7 2 Hence, z 2 - z 3 2 = 7 4 = 1 . 75

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