GATE EE 2024 | Complex Variable Question 4 | Engineering Mathematics | GATE EE - ExamSIDE.com

1

GATE EE 2024

Numerical

+1

-0

Consider the complex function $f(z) = \cos z + e^{z^2}$. The coefficient of $z^5$ in the Taylor series expansion of $f(z)$ about the origin is ______ (rounded off to 1 decimal place).

Your input ____

2

GATE EE 2021

MCQ (Single Correct Answer)

+1

-0.33

Let $P(z)=z^3+(1+j) z^2+(2+j) z+3$, where $z$ is complex number. Which one of the following is true?

A

Conjugate $\{P(z)\}=P$ (Conjugate $\{z\}$ ) for all $z$

B

The sum of the roots of $P(z)=0$ is a real number

C

The complex roots of the equation $P(z)=0$ come in conjugate pairs.

D

All the roots cannot be real

3

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

+1

-0.3

For a complex number $$z,$$
$$\mathop {Lim}\limits_{z \to i} {{{z^2} + 1} \over {{z^3} + 2z - i\left( {{z^2} + 2} \right)}}$$ is

A

$$-2i$$

B

$$-i$$

C

$$i$$

D

$$2i$$

4

GATE EE 2016 Set 2

MCQ (Single Correct Answer)

+1

-0.3

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?

A

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

B

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

C

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

D

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

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