The points , and on the Argand diagram represent the complex numbers , and respectively.

The points , , and form a square as shown on the diagram.
 

 
It is given that  .

1.  Find  .  (1 mark)
   

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2.  Find  .  (1 mark)
   

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3.  Find  .  (1 mark)
   

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The points    and    on the Argand diagram represent the complex numbers    and   respectively. The points form a square as shown on the diagram.
 

By using vectors, or otherwise, show that  .  (2 marks)

Let    where  .

On the Argand diagram the point represents  , the point represents    and the point represents  .
 

Copy or trace the diagram into your writing booklet.

1. Explain why the parallelogram    is a rhombus.   (1 mark)
   

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2. Show that  .   (1 mark)
   

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3. Show that  .   (2 marks)
   

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4. By considering the real part of  , or otherwise deduce that

5.  

       .   (1 mark) 
   

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On the Argand diagram, the complex numbers    and    form a rhombus.
 

1. Find    in the form  , where    and    are real numbers.  (1 mark)
   

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2. An interior angle, , of the rhombus is marked on the diagram.
   

    

   Find the value of   (2 marks)
   

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