Page 38 - BacII 2011-2017 by Lim Seyha

វិទយល័យសេម�ចឳ េខត�េស ម�ប 36

( ) ( )
2 1 x + 2 2 1
ង. lim ln(x + 2) – ln x – + = lim ln – +
x→+∞ x + 2 4 x→+∞ x x + 2 4
( ( ) )
2 2 1
= lim ln 1 + – +
x→+∞ x x + 2 4
1 1
= ln 1 – 0 + =
4 4
( )
2 1 1
lim ln(x + 2) – ln x – + =
x→+∞ x + 2 4 4
II. ១. ក. គណនា z 1 + z 2 , z 1 + z 3 , (z 1 + z 2 )(z 1 + z 3 )
√ √ √
យ z 1 = 2, z 2 = –i 2, z 3 = +i 2
√ ( √ ) √ √ √ √
ើងបាន z 1 + z 2 = 2 + –i 2 = 2 – i 2 z 1 + z 2 = 2 – i 2

√ √ √ √
z 1 + z 3 = 2 + i 2 z 1 + z 3 = 2 + i 2
( √ √ ) ( √
( ) ( ) √ ) 2
z 1 + z 2 z 1 + z 3 = 2 – i 2 2 + i 2 = 2 – i 2 = 4
( ) ( )
z 1 + z 2 z 1 + z 3 = 4
( ) 2
z 1 + z 3
ខ. កំណត់ម៉ូឌុល និងអាគុយម៉ង់ z 1 + z 2 , z 1 + z 3 ,
z 1 + z 2
 √ √  ( )
√ √  2 2  7π 7π
• z 1 + z 2 =   – i = 2 cos + i sin


2 – i 2 = 2 
2 2 4 4
 
7π 7π
ដូច ះ ម៉ូឌុល r = 2 ; អាគុយម៉ង់ θ = ឬ θ = + 2kπ ; k ∈ Z
4 4
 √ √ 
√ √  2 ( π π )
• z 1 + z 3 =   + i 2   = 2 cos + i sin


2 + i 2 = 2 
2 2 4 4
 
π π
ដូច ះ ម៉ូឌុល r = 2 ; អាគុយម៉ង់ θ = ឬ θ = + 2kπ ; k ∈ Z
4 4
( ) 2 ( ( ) ( )) 2 ( ) ( )
z 1 + z 3 2 π 7π π 7π –6π –6π
• = cos – + i sin – = cos 2 + i sin 2
z 1 + z 2 2 4 4 4 4 4 4
( ) ( ) ( ) ( )
= cos –3π + i sin –3π = cos –4π + π + i sin –4π + π
= cos π + i sin π
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