GATE EE 2017 Set 1 | Complex Variable Question 4 | Engineering Mathematics

Consider the function $$f\left( z \right) = z + {z^ * }$$ where $$z$$ is a complex variable and $${z^ * }$$ denotes its complex conjugate. Which one of the following is TRUE?

$$f(z)$$ is both continuous and analytic

$$f(z)$$ is continuous but not analytic

$$f(z)$$ is not continuous but is analytic

$$f(z)$$ is neither continuous nor analytic

GATE EE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ 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 differentiable at $${z_0},$$ then $$g(z)$$ & $$h(z)$$ are also differentiable at $${z_0}.$$

If $$g(z)$$ & $$h(z)$$ 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.

GATE EE 2014 Set 3

MCQ (Single Correct Answer)

-0.3

Integration of the complex function $$f\left( z \right) = {{{z^2}} \over {{z^2} - 1}},$$ in the counterclockwise direction, around $$\left| {z - 1} \right| = 1,$$ is

$$ - \pi i$$

$$0$$

$$\pi i$$

$$2\pi i$$

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Questions Asked from Marks 1

GATE EE 2024 (2) GATE EE 2017 Set 1 (1) GATE EE 2016 Set 2 (1) GATE EE 2015 Set 2 (1) GATE EE 2014 Set 3 (1) GATE EE 2014 Set 2 (1) GATE EE 2013 (1) GATE EE 2008 (1)

GATE EE Subjects

Electromagnetic Fields

Signals and Systems

Engineering Mathematics

General Aptitude

Power Electronics

Power System Analysis

Analog Electronics

Control Systems

Digital Electronics

Electrical Machines

Electric Circuits

Electrical and Electronics Measurement