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1
GATE EE 2024
MCQ (More than One Correct Answer)
+1
-0

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

A

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

B

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

C

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

D

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

2
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 ____
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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GATE EE Subjects
Electric Circuits
Three Phase Circuits Transient Response Graph Theory Two Port Networks Sinusoidal Steady State Analysis Network Elements Network Theorems
Electromagnetic Fields
Time Varying Fields Electrostatics Magnetostatics
Signals and Systems
Linear Time Invariant Systems Continuous and Discrete Time Signals Continuous Time Signal Fourier Transform Continuous Time Periodic Signal Fourier Series Discrete Time Signal Z Transformation Miscellaneous Continuous Time Signal Laplace Transform Sampling Theorem
Electrical Machines
Induction Machines D.C Machines Synchronous Machines Transformers
Engineering Mathematics
Linear Algebra Differential Equations Calculus Probability and Statistics Numerical Methods Vector Calculus Transform Theory Complex Variable
General Aptitude
Verbal Ability Logical Reasoning Numerical Ability
Power System Analysis
Per Unit System Power Generation Cost Power System Stability Symmetrical Components and Symmetrical and Unsymmetrical Faults Circuit Breaker Switch Gear and Protection Load Flow Studies High Voltage Dc Transmission Generating Power Station Parameters and Performance of Transmission Lines
Electrical and Electronics Measurement
Error Analysis and Measurement Basic of Indicating Instruments Potentiometer and Instrument Transformers Measurement of Resistance and A.C Bridges Measurement of Energy and Power Digital Voltmeters Questions Cathode Ray Oscilloscope
Analog Electronics
Diode Circuits and Applications Frequency Response Bjt and Mosfet Biasing 555 Timer Feedback Amplifiers and Oscillator Circuits Operational Amplifier Small Signal Modeling
Control Systems
Block Diagram and Signal Flow Graph Polar Nyquist and Bode Plot State Variable Analysis Basics of Control System Routh Hurwitz Stability Time Response Analysis Root Locus Techniques Controller and Compensator
Power Electronics
Choppers and Commutation Techniques Single and Three Phase Rectifier Power Semiconductor Devices Ac Voltage Controllers Inverters
Digital Electronics
Boolean Algebra Logic Gates Combinational Circuits Minimization Logic Families and Memories Sequential Circuits Analog to Digital and Digital to Analog Converter Microprocessor
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