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Example
P.M./Complex/p.2
-1 = _____________________________________________________
ln (-1) = __________________________________________________
∴ ln (-8) = __________________________________________________
Express the following complex numbers in the polar form :
(a)
2i
(b)
(1 + i)i
(c)
1 + i
2 - i
(d) (4 + i)(3 - i)
Solution
(a) ______________________________________________________________
______________________________________________________________
(b) ______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(c) ______________________________________________________________
______________________________________________________________
______________________________________________________________
(d) ______________________________________________________________
______________________________________________________________
(e) ______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
Five Arithmetic Operations
(a) Addition/ Subtraction :
z1 = x1 + i y1
and z 2 = x 2 + i y 2
where x1 , y1 , x 2 , y 2 R
 z1  z2 = (x1  x2 ) + i(y1  y2 )
(b) Multiplication :
z1  z2 = (x1 + iy 1)(x2 + iy 2 )
(x1x2 - y1y2 ) + i(x1y2 + y1x2 )
i
i
z1  z2 = r1e 1  r2e 2
i(  )
= r1r2e 1 2
=

z1z2 = r1r2
and arg z 1z2 = arg z1 + arg z 2
n and arg z n = n arg z
Note : z1n = z1
1
1

z1z2 = z1 z2
for any integer n.
(e)
i
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