GATE CE 2005 | Complex Variable Question 9 | Engineering Mathematics

GATE CE 2005

MCQ (Single Correct Answer)

-0.3

Which one of the following is not true for the complex number z₁ and z₂ ?

$${{{z_1}} \over {{z_2}}} = {{{z_1}\overline {{z_2}} } \over {{{\left| {{z_2}} \right|}^2}}}$$

$$\left| {{z_1}\, + \,\,{z_2}} \right| \le \,\left| {{z_1}} \right|\, + \,\left| {{z_2}} \right|$$

$$\left| {{z_1}\, + \,\,{z_2}} \right| \le \,\left| {\left| {{z_1}} \right|\, - \,\left| {{z_2}} \right|} \right|$$

$${\left| {{z_1}\, + \,\,{z_2}} \right|^2}\, + \,{\left| {{z_1}\, - \,\,{z_2}} \right|^2} = \,\,2{\left| {{z_1}} \right|^2}\, + \,2{\left| {{z_2}} \right|^2}$$

GATE CE 1997

MCQ (Single Correct Answer)

-0.3

$${e^z}$$ is a periodic with a period of

$$2\pi $$

$$2\pi i$$

$$\pi $$

$$i\pi $$

GATE CE Subjects

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Geomatics Engineering Or Surveying

Levelling Traversing Theodolites and Plane Table Surveying Measurement of Area, Volume and Theory of Errors and Survey Adjustment Field Astronomy and Photogrammetric Surveying Basics of GIS, GPS and Remote Sensing Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey

Engineering Mechanics

Work Energy Principle and Impulse Momentum Equation Equilibrium of Force Systems

Hydrology

Precipitation and Frequency of Rainfall Data Evaporation and Transpiration Infiltration Hydrograph Flood Estimation and Flood Routing

Transportation Engineering

Highway Devolopment and Planning Highway Geometric Design Traffic Engineering Highway Materials Pavement Design Railway, Runway and Taxiway Design

Strength of Materials Or Solid Mechanics

Pure Bending Shear Stress In Beams Simple Stresses Complex Stress Centroid and Moment of Inertia Torsion Shear Force and Bending Moment Deflection of Beams Thin Cylinder Strain Energy Method Columns and Struts Propped Cantilever Beam

Reinforced Cement Concrete

Doubly Reinforced Sections Limit State of Collapse Shear Footings Bond Slabs Limit State of Collapse Torsion Limit State of Serviceability Prestressed Concrete Singly Reinforced Sections Workmenship and Fundamentals Flanged Beams Limit State of Collapse Compression

Steel Structures

Eccentric Connections Plate Girder Tension Members Welded Connections Materials and Specifications Riveted Joints and Bolted Joints Beams Compression Members

Irrigation

Water Requirement of Crops Gravity Dams and Spillways

Environmental Engineering

Sources and Coveyances Water Quality Control of Water Treatment of Water Water Demand Waste Water Characteristics Treatment of Sewage Disposal of Sewage Effluent Solid Waste Management Air Pollution Noise Pollution

Engineering Mathematics

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

Structural Analysis

Stability and Static Indeterminacy Methods of Analysis Plastic Analysis Moment Distribution Method Indeterminacy Energy Principle Influence Line Diagram Arches and Cable Slope Deflection Method Truss Matrix Method

Geotechnical Engineering

Origin of Soils Definitions and Properties of Soils Classification of Soils and Clay Mineralogy Effective Stress and Permeability Seepage Analysis Compaction of Soil Compressibility and Consolidation Shear Strength of Soil Stress Distribution of Soil Retaining Wall and Earth Pressure Stability of Slopes Shallow Foundation Pile Foundation Soil Stabilization

Fluid Mechanics and Hydraulic Machines

Fluid Pressure and Measurement Fluid Dynamics Boundary Layer Theory Drag and Lift Flow Through Pipes Open Channel Flow Hydraulic Machines Properties of Fluids Fluid Statics

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability