Answer Key and Solutions Part A

# Answer Key and Solutions Part A - 21 SOLUTIONS 1. 1 5,2i 2...

This preview shows pages 1–4. Sign up to view the full content.

Im Re 1 2 -1 -2 1 -1 -2 (0·5,0) (-0·5,0·5) (-1,-1) (2,-2) 21. SOLUTIONS 1. Cartesian Co-ordinates 1. 5, ± 2 i . 2. -3 or 2. 3. Let  z  =  a  +  bi .  Then: bi a bi a bi a i b a - - - - + - - + ) 1 ( ) 1 ( . ) 1 ( ) 1 (     ü   2 2 ) 1 ( ) 1 ( ) 1 )( 1 ( ) 1 ( b a b b i b a abi a a + - - + - - + - -    ü The result is purely imaginary when  0 ) 1 ( ) 1 ( ) 1 ( 2 2 = + - - + - b a b b a a    ü i.e.  0 2 2 = - + - b b a a i.e.  2 1 4 1 4 1 2 2 = + - + + - b b a a    i.e.  2 1 ) 2 1 ( ) 2 1 ( 2 2 = - + - b a   ü This equation represents a circle with centre  ) 2 1 , 2 1 (   ü   and radius =  2 1 .   ü 2. Polar Co-ordinates 1. (a) i w z 2 2 4 3 2 2 4 3 3 - + + = +    (b)    - 12 12 π cis     (c) 12 5 4 3 cis 2. (a) 4 2 cis z = cis w 3 = (b)     - 4 2 6 cis (c)    i 5 1 5 3 - - 3. (a) z 2  +  z  – 1 (b) ) 3 ( , 3 , 1 3 2 1 - = = - = cis z cis z z   are the associated values 2 5 2 1 4 + - = z , 2 5 2 1 5 - - = z   are the remaining values. 4. Q and R are   i and i 2 3 - + - = 5. ) 12 ( 18 - cis   or   ) 12 7 ( 18 cis 6. (a) graph (b) n n z z 2 1 = + (c) n = 8. VET Calculus 135 21.Solutions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
VET Calculus 136 21.Solutions
7. (a) z  = 1 - i 3  = 2 cis (- 3 π ) ü   and    w  = 2 cis  6 . Then  wz  = 4 cis (- 6 )   üü Alternatively z  = 1 - i 3  and  w  = 2 cis  6  =  3  +  i  .  ( ü ) Then  wz  = 2 3  - 2 i .  ( ) (b)     Im ( z )     Re ( z )      - 3 z                wz

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

Answer Key and Solutions Part A - 21 SOLUTIONS 1. 1 5,2i 2...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online