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Question: Answered & Verified by Expert
Let z1=1, z2=2, z3=3 and z1+z2+z3=3+5i, then the value of Rez1z2-+z2z3-+z3z1- is equal to (Where z1, z2 and z3 are complex numbers)
MathematicsComplex NumberJEE Main
Options:
  • A 1
  • B -1
  • C -12
  • D 0
Solution:
2227 Upvotes Verified Answer
The correct answer is: 0
z1+z2+z32=32+5=14
⇒z1+z2+z3z1-+z2-+z3-=14
⇒z12+z22+z32+z1z2-+z2z3-+z3z1-+z1-z2+z2-z3+z3-z1=14
⇒1+4+9+2 Rez1z2-+z2z3-+z3z1-=14
⇒2 Rez1z2-+z2z3-+z3z1-=0
⇒ Rez1z2-+z2z3-+z3z1-=0

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