Please check if the following equations are coect: ( ) ( )( ) ( )1121 1 222 1 212 212 2j jj jAa b...

Question

Please check if the following equations are co
ect:

( ) ( )
( ) ( )
1
1
2
1 1 2
2
2 1 2
1
2 2
1
2 2
j j
j j
Aa b jb e je
Aa b jb je e
φ φ
φ φ
 = + = +

 = + = +

,

equals to:

( )
( )
( )
1
2
1 2
2
2
sin
2
2
2
cos
2
jja Ae e
a
φ π
φ
φ π
φ π
∆ +
 ∆ + 
  
    =   ∆ +        

cal0102-sd2mznmq.pdf

Baljit · Accepted Answer

Microsoft Word - Document1
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Answer: - 
Now we have equation 
?
? = √2 ? ?
 ?   
⎣
⎢
⎢
⎢
⎢
⎢
⎡
sin
Δ? +
Π
2
2
cos
Δ? +
Π
2
2
⎦
⎥
⎥
⎥
⎥
⎥
⎤

Now we know that 
sin ? =
? − ?
2?
 
 cos ? =
? + ?
2

Now by using these trigonometric identities in our equation 
?
? = √2 ? ?
  ?   
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎡
? − ?
2?
? + ?
2 ⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎤
 
Now applying matrix multiplication 
?
? =   
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡
√2 ? ?   ?
⎝
⎜⎜
⎛? − ?
2?
⎠
⎟⎟
⎞
√2 ? ?   ?
⎝
⎜⎜
⎛? + ?
2
⎠
⎟⎟
⎞
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎤

?
? =   
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎡
√2
2?
 ? ?   ?
⎝
⎜
⎛
? − ?

Please check if the two expressions agree with each other or not. A clear derivation of the correlation must be written and provided.

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