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Title: Complex Varibles
Description: You can find nice and helping,handwritten notes of complex variables

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Assignment-1

1
1
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2
2
...

3
...

1

4
...
R
...

5
...

6
...

7
...

8
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Find the values of C1 and C2 such that the function f(z)=x2+C1y2-2xy+i(C2x2-y2+2xy)
is
...

10
...

11
...
How would you explain this?
12
...

13
...

14
...
Find the analytic function for
which e x ( x cos y  y sin y ) is imaginary part
...
If f ( z )  u  iv is an analytic function of z and u  v 
f ( z) 

cos x  sin x  e y )
, prove that
2cos x  2cosh y

1
z

1  cot 2  when f ( 2 )  0
...

zz  x y 
 2
2 
17
...

 x y 
16
...
If f ( z ) is constant, prove that f(z)is also constant
...
If f(z) is regular function of z, prove that ( 𝜕𝑥 2 +

𝜕2
𝜕𝑦 2

) |𝑓(𝑧)|2 = 4|𝑓′(z)|2
Title: Complex Varibles
Description: You can find nice and helping,handwritten notes of complex variables