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Complex Numbers, EXT2 N1 2020 HSC 13d

  1. Show that for any integer ,  .   (1 mark)

  2. By expanding    show that
     
       .   (3 marks)

  3. Hence, or otherwise, find  .   (2 marks)

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i.     
   
   

 

ii.   
   

 


 

 

iii.   
   
   
   
   

Calculus, EXT2 C1 2015 HSC 14a

  1. Differentiate  , expressing the result in terms of    only.  (2 marks)

  2. Hence, or otherwise, deduce that
     
         ,  for   (2 marks) 

  3. Find    (1 mark)

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i.   

 

ii.  

 

iii.  
   
     
   

Calculus, EXT2 C1 2011 HSC 7b

Let   

  1. Use the substitution    to show that
     
            (2 marks)

     

  2. Hence, find the value of  .  (3 marks)

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i.   

 
 
 

 

ii.  

 

 

 

♦ Mean mark 36%.