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let z=cos(theta)+i.sin(theta)/(cos theta – i.sin theta), theta lies between pi/2 to pi/4. Then arg z is 2theta 2theta – pi pi + 2theta none of these

let z=cos(theta)+i.sin(theta)/(cos theta – i.sin theta),
theta lies between pi/2 to pi/4. Then arg z is
 
  1. 2theta
  2. 2theta – pi
  3. pi + 2theta
  4. none of these

Grade:11

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
6 years ago
Dear Student,
Rationalize Z and on simplification you will get,

z = cos (2theta) + i sin (2theta)
Now, arg z = tan-1 (tan (2theta)),
Since theta varies from pi/4 to pi/2.
Therefore 2theta varies from pi/2to pi.
Therfore , arg z = 2theta – pi Answer.

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