GATE EE 2024 | Complex Variable Question 3 | Engineering Mathematics

GATE EE 2024

MCQ (More than One Correct Answer)

-0

Which of the following complex functions is/are analytic on the complex plane?

$f(z) = j\text{Re}(z)$

$f(z) = \text{Im}(z)$

$f(z) = e^{|z|}$

$f(z) = z^2 - z$

GATE EE 2024

Numerical

-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 ____

GATE EE 2021

MCQ (Single Correct Answer)

-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?

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

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

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

All the roots cannot be real

GATE EE 2017 Set 1

MCQ (Single Correct Answer)

-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

$$-2i$$

$$-i$$

$$i$$

$$2i$$

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