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Question: Answered & Verified by Expert
If z1, z2 and z3 are three complex numbers such that  z 1 = z 2 = z 3 = 1 z 1 + 1 z 2 + 1 z 3 = 1 , then z1+z2+z3 is 
MathematicsComplex NumberJEE Main
Solution:
2421 Upvotes Verified Answer
The correct answer is: 1
z 1 = z 2 = z 3 = 1  (given)

Now z1=1⇒z12=1⇒z1z1¯=1 ⇒1z1=z1¯

Similarly, 1z2=z2¯ & 1z3=z3¯

Now 1 z 1 + 1 z 2 + 1 z 3 = 1

⇒z1+z2+z3¯=1 (∵z1¯+z2¯=z1+z2¯)

and |z1+z2+z3¯|=1  (∵|z1¯|=|z|)

⇒ z 1 + z 2 + z 3 = 1

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