F(z) is a function of the complex variable z = x + iy given

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F(z) is a function of the complex variable z = x + iy given by
F(z) = iz + k Re(z) + i Im(z)
For what value of k will F(z) satisfy the Cauchy Riemann equations?

1. 0
2. 1
3. –1
4. y

Correct Option: B

By Cauchy -Riemann equations
u_x = v_y
u + iv = i (x + iy) + kx + iy
u + iv = kx – y + i (x + y)
u = kx – y, v = x + y
u_x = k, u_y = –1
v = x + y
v_x = 1; v_y = 1
u_x = v_y
k = 1