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Manipal MET2018MathematicsComplex Number

Area of the triangle in the argand diagram formed by the complex numbers z, i z, z+i z , where z=x+i y is

Options

  1. A|z|
  2. B|z|^2
  3. C2|z|^2
  4. D1 2 |z|^2

Correct answer

D. 1 2 |z|^2

Step-by-step solution

Since, i z=z e^ i / 2 This implies that i z is the vector obtained by rotating vector z in anticlock wise direction through 90^ . O A A B So, area of O A B= 1 2 O A O B= 1 2 |z||i z|= 1 2 |z|^2

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