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Complex Numbers, EXT2 N1 2005 HSC 2b

Let  .

  1. Express    in modulus-argument form.   (2 marks)

  2. Express    in modulus-argument form.   (2 marks)

  3. Hence express    in the form  .   (1 mark)

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i.   
 

 

 

ii.  
   
   

 

iii.  
   
   

Complex Numbers, EXT2 N1 2008 HSC 2b

  1. Write    in the form  , where and are real.  (2 marks)

  2. By expressing both    and    in  modulus-argument form, write    in modulus-argument form.   (3 marks)

  3. Hence find    in surd form.  (1 mark)

  4. By using the result of part (ii), or otherwise, calculate  .   (1 mark)

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i.     
   
   

 

ii.   


  


 


 

 
 

 

iii. 

 

 

iv.     
   
   

Complex Numbers, EXT2 N1 2015 HSC 12a

The complex number is such that  and  

Plot each of the following complex numbers on the same half-page Argand diagram.

  1.     (1 mark)

  2.     (1 mark)

  3.     (1 mark)

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i.   ­
­

 

ii.   ­
­
­

COMMENT: 12a(iii) had the lowest mean mark (55%) of any part within Q12 and deserves attention.
iii.  ­
­
­

Complex Numbers, EXT2 N1 2012 HSC 11d

  1. Write    in modulus-argument form.  (2 marks)

  2. Hence express    in the form  , where and are real.  (1 mark)

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i.
 

 

   
   

 

ii.  
   
   
   
   

Complex Numbers, EXT2 N1 2013 HSC 11a

Let    and 

  1. Find    (1 mark)
  2. Express in modulus–argument form.  (2 marks)
  3. Write in its simplest form.  (2 marks)
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i.   

 

 

ii.   
 
 
 
MARKER’S COMMENT: The directive “in its simplest form” required students to convert to 1.

 

iii.