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Engineering Maths · Q61

Complex Variable

Engineering and GATE · Engineering Maths · question 61

Q61

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?

A.
If f(z) is differentiable at z0, then g(z) and h(z) are also differentiable at z0
B.
If g(z) and h(z) are differentiable at z0, then f(z) is also differentiable at z0
Answer
C.
If f(z) is continuous at z0, then it is differentiable at z0
D.
If f(z) is differentiable at z0, then so are its real and imaginary parts

Answer: Option B

Solution

Answer: Option B
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