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JEE Main202117 Mar 2021Morning ShiftMathematicsComplex NumberActual

The area of the triangle with vertices P ( z ) , Q ( i z ) and R ( z + i z ) is

Options

  1. A1
  2. B1 2 | z | 2
  3. C1 2
  4. D1 2 | z + i z | 2

Correct answer

B. 1 2 | z | 2

Step-by-step solution

From the above diagram, it is clear that z ,   i z are perpendicular to each other. Here, base = z , height = i z So, area of the triangle formed by the vertices i.e., A = 1 2 × base × height ⇒ A = 1 2 × z × i z ⇒ A = 1 2 z 2 Hence, the required area is 1 2 z 2 .

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