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Complex Plane, Modulus, Argument, and Graphical Representation of a Complex Number Hello, my name is Mohammad Ali Nayeem, a student at DIU studying Software Engineering. In Math 102, we delve into various concepts related to complex numbers, including the complex plane, modulus, argument, and their graphical representation. Complex Plane The complex plane is a two-dimensional plane used to visually represent complex numbers. It consists of a horizontal axis (the real axis) and a vertical axis (the imaginary axis). Any complex number 𝑧 = 𝑎 + 𝑏 𝑖 z=a+bi can be plotted on this plane, where 𝑎 a is the real part and 𝑏 b is the imaginary part. Modulus The modulus (or absolute value) of a complex number 𝑧 = 𝑎 + 𝑏 𝑖 z=a+bi is the distance of the point representing 𝑧 z from the origin (0, 0) in the complex plane. It is denoted by ∣ 𝑧 ∣ ∣z∣ and calculated using the formula: ∣ 𝑧 ∣ = 𝑎 2 + 𝑏 2 ∣z∣= a 2 +b 2 The modulus provides a measure of the magnitude of the complex number. Argument The argument of a complex number is the angle 𝜃 θ between the positive real axis and the line segment connecting the origin to the point representing the complex number. It is denoted by arg ( 𝑧 ) arg(z) and is usually measured in radians. The argument can be found using the formula: 𝜃 = tan − 1 ( 𝑏 𝑎 ) θ=tan −1 ( a b ) The argument indicates the direction of the complex number in the complex plane. Graphical Representation To graphically represent a complex number 𝑧 = 𝑎 + 𝑏 𝑖 z=a+bi, plot the point ( 𝑎 , 𝑏 ) (a,b) on the complex plane. The modulus is the length of the line from the origin to this point, and the argument is the angle this line makes with the positive real axis. For example, the complex number 3 + 4 𝑖 3+4i can be plotted as the point (3, 4). Its modulus is: ∣ 3 + 4 𝑖 ∣ = 3 2 + 4 2 = 5 ∣3+4i∣= 3 2 +4 2 =5 Its argument is: 𝜃 = tan − 1 ( 4 3 ) ≈ 0.93 radians θ=tan −1 ( 3 4 )≈0.93 radians Understanding these concepts helps in visualizing and manipulating complex numbers, which are fundamental in many areas of engineering and applied mathematics. Best regards, Mohammad Ali Nayeem DIU Software Engineering Student

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原版一模一样【微信：741003700 】【(csu毕业证书)查尔斯特大学毕业证硕士学历】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
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留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

Modelagem de um CSTR com reação endotermica.pdf

Modelagem em função de transferencia. CSTR não-linear.

5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...

Bigdata of technology

Low power architecture of logic gates using adiabatic techniques

The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.

一比一原版(UMich毕业证)密歇根大学|安娜堡分校毕业证成绩单专业办理

UMich毕业证原版定制【微信：176555708】【密歇根大学|安娜堡分校毕业证成绩单-学位证】【微信：176555708】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
◆◆◆◆◆ — — — — — — — — 【留学教育】留学归国服务中心 — — — — — -◆◆◆◆◆
【主营项目】
一.毕业证【微信：176555708】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【微信：176555708】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
学历顾问：微信：176555708

Heap Sort (SS).ppt FOR ENGINEERING GRADUATES, BCA, MCA, MTECH, BSC STUDENTS

HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.

PROJECT FORMAT FOR EVS AMITY UNIVERSITY GWALIOR.ppt

Ppt on evs amity University project work.........................??????!?!?!?!!?!!?!!?/?/?/?/?/?

BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf

Guia para el codigo ASME

Unbalanced Three Phase Systems and circuits.pptx

Unbalanced three phase systems

Advanced control scheme of doubly fed induction generator for wind turbine us...

This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.

Building Electrical System Design & Installation

Guide for Building Electrical System Design & Installation

A review on techniques and modelling methodologies used for checking electrom...

The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.

一比一原版(UC Berkeley毕业证)加利福尼亚大学|伯克利分校毕业证成绩单专业办理

UC Berkeley毕业证原版定制【微信：176555708】【加利福尼亚大学|伯克利分校毕业证成绩单-学位证】【微信：176555708】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
◆◆◆◆◆ — — — — — — — — 【留学教育】留学归国服务中心 — — — — — -◆◆◆◆◆
【主营项目】
一.毕业证【微信：176555708】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【微信：176555708】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
学历顾问：微信：176555708

22CYT12-Unit-V-E Waste and its Management.ppt

Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.

Understanding Inductive Bias in Machine Learning

This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.

ACEP Magazine edition 4th launched on 05.06.2024

This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.

6th International Conference on Machine Learning & Applications (CMLA 2024)

6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.

Swimming pool mechanical components design.pptx

swimming pool mechanical design

哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样

哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样

Modelagem de um CSTR com reação endotermica.pdf

Modelagem de um CSTR com reação endotermica.pdf

5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...

5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...

Low power architecture of logic gates using adiabatic techniques

Low power architecture of logic gates using adiabatic techniques

一比一原版(UMich毕业证)密歇根大学|安娜堡分校毕业证成绩单专业办理

一比一原版(UMich毕业证)密歇根大学|安娜堡分校毕业证成绩单专业办理

Heap Sort (SS).ppt FOR ENGINEERING GRADUATES, BCA, MCA, MTECH, BSC STUDENTS

Heap Sort (SS).ppt FOR ENGINEERING GRADUATES, BCA, MCA, MTECH, BSC STUDENTS

PROJECT FORMAT FOR EVS AMITY UNIVERSITY GWALIOR.ppt

PROJECT FORMAT FOR EVS AMITY UNIVERSITY GWALIOR.ppt

BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf

BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf

Unbalanced Three Phase Systems and circuits.pptx

Unbalanced Three Phase Systems and circuits.pptx

Advanced control scheme of doubly fed induction generator for wind turbine us...

Advanced control scheme of doubly fed induction generator for wind turbine us...

Building Electrical System Design & Installation

Building Electrical System Design & Installation

A review on techniques and modelling methodologies used for checking electrom...

A review on techniques and modelling methodologies used for checking electrom...

PPT on GRP pipes manufacturing and testing

PPT on GRP pipes manufacturing and testing

一比一原版(UC Berkeley毕业证)加利福尼亚大学|伯克利分校毕业证成绩单专业办理

一比一原版(UC Berkeley毕业证)加利福尼亚大学|伯克利分校毕业证成绩单专业办理

Self-Control of Emotions by Slidesgo.pptx

Self-Control of Emotions by Slidesgo.pptx

22CYT12-Unit-V-E Waste and its Management.ppt

22CYT12-Unit-V-E Waste and its Management.ppt

Understanding Inductive Bias in Machine Learning

Understanding Inductive Bias in Machine Learning

ACEP Magazine edition 4th launched on 05.06.2024

ACEP Magazine edition 4th launched on 05.06.2024

6th International Conference on Machine Learning & Applications (CMLA 2024)

6th International Conference on Machine Learning & Applications (CMLA 2024)

Swimming pool mechanical components design.pptx

Swimming pool mechanical components design.pptx

- 1. Complex plane, Modulus, Argument, Complex plane, Modulus, Argument, Graphical representation of a Graphical representation of a complex number. complex number. P r e s e n t a t i o n o n Submitted To Mr. Md. Mozammelul Haque Lecturer Department of Software Engineering Daffodil International University
- 2. Section : A ID : 232-35-016 Reduan Ahmad Section : A ID : 232-35-003 Abdullah Al Noman Section : A ID : 232-35-022 Mohammad Ali Nayeem Section : A ID : 222-35-1189 Sabbir Hossen Section : A ID : 232-35-001 Prionti Maliha
- 3. Learning Target: Complex plane Modulus Argument Graphical representation of a complex number.
- 4. Number Line Negative Numbers (−) Positive Numbers (+)
- 5. A plane for complex numbers! 3 units along (the real axis), 4 units up (the imaginary axis). Plot a complex number like 3 + 4i
- 6. Modulus The modulus of a complex number is a fundamental concept in mathematics. The modulus of a complex number is the distance of the complex number from the origin in the the complex plane The modulus of a complex number (z), denoted as |z|, is the non-negative value equal to the square root of the sum of the squares of its real (x) and imaginary (y) parts, expressed as: In this equation, 𝑥 and 𝑦 represent the real and imaginary components of the complex number 𝑧 respectively. When a complex number (z) is plotted on a graph (the complex plane), the distance between the coordinates of the complex number and the origin (0, 0) is called the modulus of the complex number. Modulus of a complex number is always non-negative
- 7. Examples Now lets Find Modulus of |z|=3 + 4i
- 8. Arguments in the Complex Plane complex plane with a vector representing the complex number 3 + 4i
- 9. Argument of Complex Numbers Formula θ = tan⁻¹ (y/x) θ = π - tan⁻¹ |y/x| θ = π + tan⁻¹ |y/x| θ = 2π - tan⁻¹ |y/x|
- 10. Calculating the Argument Be mindful of the quadrant of the complex number to determine the correct value of θ. Formula: For z = x + yi, the argument θ is given by: tan(θ) = y/x θ = arctan(y/x) (using the inverse tangent function)
- 11. Examples Identify: x = 3 and y = 4 Calculate: tan(θ) = 4/3 Solve: θ = arctan(4/3) (using a calculator) Result: θ ≈ 53.13° (first quadrant)
- 13. We can represent complex numbers in the complex plane. We use the horizontal axis for the real part and the vertical axis for the imaginary part.
- 14. Example : The number 3+2𝑗 (where 𝑗=−1 ) is represented by:
- 15. The point A is the representation of the complex number 3+2𝑗. The horizontal axis is marked R (for the "real" numbered-component), and the vertical axis is marked j (for the imaginary component of the complex number).
- 16. THANK YOU!