If z1,z2 and z3 are 3 distinct complex numbers such that (3/|z1 - z2|)=(5/|z2 - z3|)=(7/|z3 - z1|) , then the value of (9/z1 - z2)+(25/z2 - z3)+(49/z3 - z1) is equal to

Question

If z1,z2 and z3 are 3 distinct complex numbers such that (3/|z1 - z2|)=(5/|z2 - z3|)=(7/|z3 - z1|) , then the value of (9/z1 - z2)+(25/z2 - z3)+(49/z3 - z1) is equal to (A) 0 (B) 1 (C) -1 (D) 15

Tardigrade Admin · Accepted Answer

Let, (3/|z1-z2|)=(5/|z2-z3|)=(7/|z3-z1|)=k (9/|z1-z2|2)=(25/|z2-z3|2)=(49/|z3-z1|2)= k 2 ⇒ (9/(z1-z2)( barz1- barz2))=k2 ⇒ (9/z1-z2)=k2( barz1- barz2) similarly, (25/(z2-z3))=k2( barz2- barz3) and (49/(z3-z1))=k2( barz3- barz1) ⇒ (9/z1-z2)+(25/z2-z3)+(49/z3-z1) =k2( barz1- barz2+ barz2- barz3+ barz3- barz1)=0

$0$

$1$

$- 1$

$15$

Q. If z1​,z2​ and z3​ are 3 distinct complex numbers such that ∣z1​−z2​∣3​=∣z2​−z3​∣5​=∣z3​−z1​∣7​ , then the value of z1​−z2​9​+z2​−z3​25​+z3​−z1​49​ is equal to

0

1

−1

15

$0$

$1$

$- 1$

$15$