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BITSAT 2015
Exam
BITSAT
Year
2015
Subject
Mathematics
Chapter
Complex Number

BITSAT 2015 · Mathematics · Complex Number

If complex number z_ 1 , z_ 2 and 0 are vertices of equilateral...

If complex number z1,z2z_{1}, z_{2} and 0 are vertices of equilateral triangle, then z12+z22−z1z2z_{1}^{2}+z_{2}^{2}-z_{1} z_{2} is equal to

Options

  1. A00
  2. Bz1−z2z_{1}-z_{2}
  3. Cz1+z2z_{1}+z_{2}
  4. D1

Correct answer

A. 00

Step-by-step solution

z1,z2,0z_{1}, z_{2}, 0 are vertices of an equilateral triangle, so we have z12+z22+02=z1z2+z2⋅0+0⋅z1⇒z12+z22=z1z2⇒z12+z22−z1z2=0z_{1}^{2}+z_{2}^{2}+0^{2}=z_{1} z_{2}+z_{2} \cdot 0+0 \cdot z_{1} \Rightarrow z_{1}^{2}+z_{2}^{2}=z_{1} z_{2} \Rightarrow z_{1}^{2}+z_{2}^{2}-z_{1} z_{2}=0
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