Download Quiz on Complex Number 03092006

Quiz on Complex Number
03092006
1. Simplify (a) (1+2i) – (-2+4i) + (5-6i)
(b) (3-2i) (5+3i)
2. If
1 + 2i
(c)
4i
3  2i
is a root of x 2  ax  b  0 , find the values of a and b .
3. Solve z 2  (3  i) z  (2  i)  0
4. Given that w 
1 5 i
.
2
(a) Show that 2 w 2  2 w  3. .
(b) Hence evaluate w 9 (1  w 
5. Express the following complex numbers in polar forms:
(a) -2i
(b) 3 – 3i
(c)  4  4 3 i
6. Find the modulus of the following complex numbers:
(a) z  (1  i) 3 (2  i) 4 (3  i) 5
(b)
z
(3  i ) 5 (1  3i ) 6
[ 5 (1  i )] 9
7. Let z1 and z 2 C be such that z1 
Prove that if z 2  1  2i , then
7  z2
1  z2
| z2 |
 2.
| z1 |
2
.
1 10
) .
w