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Question
If the comlex numbers z1,z2,z3 represent the vertices of an equilateral triangle such that ∣z1∣=∣z2∣ =∣z3∣, then
z1+z2+z3=
If the comlex numbers z1,z2,z3 represent the vertices of an equilateral triangle such that ∣z1∣=∣z2∣ =∣z3∣, then
z1+z2+z3=
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Solution
The correct option is A 0
Let the complex number z1,z2,z3 denote the vertices A,B,C of an equilateral triangle ABC.
Then,if o be the origin,we have O¯A=z1,O¯B=z2,O¯C=z3
Therefore ∣ z1∣=∣ z2∣ z3∣ ⇒ OA=OB+OC i.e, O is the circumcentre of △ ABC.Hence
z1+z2+z3=0.
Let the complex number z1,z2,z3 denote the vertices A,B,C of an equilateral triangle ABC.
Then,if o be the origin,we have O¯A=z1,O¯B=z2,O¯C=z3
Therefore ∣ z1∣=∣ z2∣ z3∣ ⇒ OA=OB+OC i.e, O is the circumcentre of △ ABC.Hence
z1+z2+z3=0.
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