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NIELIT 2018-23

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If $w=f(z)=u(x,y)+i \: v(x,y)$ is an analytic function, then $\frac{dw}{dz}$ is:

  1. $\frac{ \partial u } {\partial x}- i \frac{ \partial u}{\partial y}$
  2. $\frac{ \partial u } {\partial x}+ i \frac{ \partial v}{\partial y}$
  3. $\frac{ \partial u } {\partial x}- i \frac{ \partial v}{\partial x}$
  4. $\frac{ \partial u } {\partial x}+ i \frac{ \partial u}{\partial y}$
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