Complex Numbers 4 Question 16

16. Show that the area of the triangle on the argand diagram formed by the complex number z,iz and z+iz is 12|z|2.

(1986, 212 M)

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Solution:

  1. We have, iz=zeiπ/2. This implies that iz is the vector obtained by rotating vector z in anti-clockwise direction through 90. Therefore, OAAB. So,

Area of OAB=12OA×OB=12|z||iz|=12|z|2



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