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
- A1
- B1 2 | z | 2
- C1 2
- 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 .