GATE Electrical Engineering (EE) 2015 Shift 2 Solved Paper

Question : 11 of 65

Marks: +1, -0

Given

f (z) = g (z) + h (z)

, where f, g, h are complex valued functions of a complex variable z. which one of the following statements is TRUE?

If $f (z)$ is differential at $z_{0}$ , then $g (z)$ and $h (z)$ are also differentiable at $z_{0}$ .
If $g (z)$ and $h (z)$ are differentiable at $z_{0}$ , then $f (z)$ is also differentiable at $z_{0}$ .
If $f (z)$ is continuous at $z_{0}$ , then it is differentiable at $z_{0}$ .
If $f (z)$ is differentiable at $z_{0}$ , then so are its real and imaginary parts.

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