Question
F(z) is a function of the complex variable z = x +iy given by
πΉ(π§) = π π§ + π π π(π§) + π πΌπ(π§).
For what value of k will F z( ) satisfy the Cauchy-Riemann equations?
Options :
0
1
-1
y
Answer :
1
Solution :
z = x + iy
Let F(z) = u + iv
F(z) = iz + k Re(z) + i Im(z) = i (x + iy ) + kx + iy = i (x + y) + (kx β y)
u = (kx β y), v = (x + y)
Using Cauchy Riemann equations:
 is a function of the complex variable z = x + iy given-1717702739551.png){kind=small}
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