Sketch the region defined by    and  .   (3 marks)

The complex numbers and both have modulus 1, and  , where denotes the principal argument.

For real numbers and , consider the complex number .

On an -plane, clearly sketch the region that contains all points for which .

A shaded region on a complex plane is shown.
 

Let be the region in the complex plane defined by    and  .

Which diagram best represents the region ?
 

Sketch the region of the complex plane defined by    where    is the principal argument of .   (3 marks)

Sketch the region in the complex plane where the inequalities

  and 

hold simultaneously.   (3 marks)

Sketch the region on the Argand diagram where the inequalities

      and 

hold simultaneously.   (3 marks)

Sketch the region defined by    and  .  (2 marks)