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

$$-2i$$

$$-i$$

$$i$$

$$2i$$

GATE EE Subjects

Browse all chapters by subject

Electric Circuits

Network Elements Network Theorems Three Phase Circuits Transient Response Sinusoidal Steady State Analysis Graph Theory Two Port Networks

Electrical Machines

Induction Machines D.C Machines Synchronous Machines Transformers

Engineering Mathematics

Vector Calculus Calculus Transform Theory Probability and Statistics Differential Equations Linear Algebra Numerical Methods Complex Variable

Signals and Systems

Continuous Time Signal Fourier Transform Miscellaneous Discrete Time Signal Z Transformation Continuous Time Periodic Signal Fourier Series Continuous and Discrete Time Signals Continuous Time Signal Laplace Transform Linear Time Invariant Systems Sampling Theorem

Power Electronics

Single and Three Phase Rectifier Inverters Power Semiconductor Devices Ac Voltage Controllers Choppers and Commutation Techniques

Power System Analysis

Circuit Breaker Parameters and Performance of Transmission Lines Switch Gear and Protection High Voltage Dc Transmission Symmetrical Components and Symmetrical and Unsymmetrical Faults Load Flow Studies Per Unit System Power Generation Cost Power System Stability Generating Power Station

Digital Electronics

Boolean Algebra Logic Gates Combinational Circuits Minimization Logic Families and Memories Sequential Circuits Analog to Digital and Digital to Analog Converter Microprocessor

Analog Electronics

Diode Circuits and Applications Bjt and Mosfet Biasing Small Signal Modeling Feedback Amplifiers and Oscillator Circuits Operational Amplifier Frequency Response 555 Timer

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Control Systems

Time Response Analysis Block Diagram and Signal Flow Graph Polar Nyquist and Bode Plot State Variable Analysis Root Locus Techniques Basics of Control System Routh Hurwitz Stability Controller and Compensator

Electrical and Electronics Measurement

Potentiometer and Instrument Transformers Measurement of Resistance and A.C Bridges Measurement of Energy and Power Cathode Ray Oscilloscope Digital Voltmeters Questions Basic of Indicating Instruments Error Analysis and Measurement

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability