[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-657321-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-657321-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","the-argand-diagram-73","The Argand diagram - 7.3","","This document provides a clear, instructional guide to understanding and constructing Argand diagrams, a fundamental tool for the pictorial representation of complex numbers. It details the mapping of a complex number z = a + bj onto a two-dimensional Cartesian plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. The content includes a step-by-step explanation of point plotting and features a practical example demonstrating the placement of various complex numbers, including purely real, purely imaginary, and complex conjugate pairs. Designed for engineers and students, this resource offers a foundational mathematical approach to visualizing complex number properties, such as the symmetrical positioning of conjugates across the real axis. It serves as an essential reference for those looking to enhance their analytical understanding of complex arithmetic through geometric interpretation.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/the-argand-diagram-73/657321/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/the-argand-diagram-73/657321.png","ImageObject",300,407,{"name":42,"@type":43},"Fishy","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":30},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What is an Argand diagram?","Question",{"text":62,"@type":63},"An Argand diagram is a pictorial representation of complex numbers where the real part is plotted on the horizontal axis (real axis) and the imaginary part is plotted on the vertical axis (imaginary axis).","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How is a complex number z = a + bj plotted on an Argand diagram?",{"text":67,"@type":63},"A complex number z = a + bj is plotted as a point with coordinates (a, b) on the diagram.",{"name":69,"@type":60,"acceptedAnswer":70},"Where do purely real and purely imaginary numbers lie on an Argand diagram?",{"text":71,"@type":63},"Purely real numbers lie on the horizontal real axis, while purely imaginary numbers lie on the vertical imaginary axis.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},657321,1792977388,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":30,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":22,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":30},14431098389841,"https://eur-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","7 .3  \nThe Argand diagram  \nIntroduction .  \nEngineers often find a pictorial representation of complex numbers useful.  \nSuch a representation is known as an Argand diagram. This leaflet explains how to draw an Argand diagram.  \n1 . The Argand diagram .  \nThe complex number z = a + bj is plotted as a point with coordinates (a, b) as shown. Because the real part of z is plotted on the horizontal axis we often refer to this as the real axis. The imaginary part of z is plotted on the vertical axis and so we refer to this as the imaginary axis. Such a diagram is called an Argand diagram.  \nimaginary axis  \nb  \n(a, b)  \nz = a + bj  \nO a  \nreal axis  \nThe complex number z = a + bj is plotted as the point with coordinates (a, b) .  \nExample  \nPlot the complex numbers 2 + 3j , −3 + 2j , −3 − 2j, 2 − 5j, 6, j on an Argand diagram.  \nSolution  \nThe figure below shows the Argand diagram. Note that purely real numbers lie on the real axis. Purely imaginary numbers lie on the imaginary axis. Note that complex conjugate pairs such as −3 ± 2j lie symmetrically on opposite sides of the real axis.  \nimaginary axis  -3+2j    \nj  \n2+3j  \n6  \n0  real axis  \n-3-2j    \n-5   \n 2-5j  \n[www.mathcentre.ac.uk 7.3.1](www.mathcentre.ac.uk 7.3.1) 􀀍c Pearson Education Ltd 2000","cbCaikpYC8qTq0dX","https://ap.wps.com/l/cbCaikpYC8qTq0dX","pdf",104374,"English","# The Argand diagram\n## Introduction\n## Definition and construction\n## Plotting examples","[{\"question\":\"What is an Argand diagram?\",\"answer\":\"An Argand diagram is a pictorial representation of complex numbers where the real part is plotted on the horizontal axis (real axis) and the imaginary part is plotted on the vertical axis (imaginary axis).\"},{\"question\":\"How is a complex number z = a + bj plotted on an Argand diagram?\",\"answer\":\"A complex number z = a + bj is plotted as a point with coordinates (a, b) on the diagram.\"},{\"question\":\"Where do purely real and purely imaginary numbers lie on an Argand diagram?\",\"answer\":\"Purely real numbers lie on the horizontal real axis, while purely imaginary numbers lie on the vertical imaginary axis.\"}]","The Argand diagram - 7.3 | PDF"]