{"id":83470,"date":"2022-12-24T17:24:21","date_gmt":"2022-12-24T14:24:21","guid":{"rendered":"https:\/\/azbuki.bg\/?p=83470"},"modified":"2025-09-16T17:09:35","modified_gmt":"2025-09-16T14:09:35","slug":"complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex","status":"publish","type":"post","link":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/","title":{"rendered":"Complex Solutions to Quadratic Inequalities and Their Modeling by Means of LATEX"},"content":{"rendered":"<p><strong>Aslanbek Khamidovitch Naziev<\/strong><br \/>\n<em>Ryazan State University named for S. A. Esenin, Ryazan \u2013 Ryazan (Russian Federation)<\/em><br \/>\n<em>Ryazan Institute for Education Development \u2013 Ryazan (Russian Federation)<\/em><\/p>\n<p><a href=\"https:\/\/doi.org\/10.53656\/math2022-6-1-com\" target=\"_blank\" rel=\"noopener noreferrer\">https:\/\/doi.org\/10.53656\/math2022-6-1-com<\/a><\/p>\n<p><strong>Abstract.<\/strong> Many people think that inequalities cannot be considered over the field\u00a0 <strong>C<\/strong> of complex numbers. And really, on <strong>C<\/strong> does not possess an order to make it an ordered field. But other orders exist and can be successfully used for getting answers to some questions which remain unanswered if restricted to the domain of real numbers. The paper notes some discordance in the behavior of the sets of solutions to quadratic equations and inequalities over the field of real numbers. These sets change when the discriminant changes until it is positive, but remain unchanged as soon as discriminant becomes negative. To overcome this oddity, it is suggested to make an exit to the complex plane with some order on it. The consequences of this action are proven, and illustrated by the dynamic model proposed in the work. The model is constructed with the help of LATEX.<br \/>\n<em>Keywords:<\/em> ordering complex numbers; reduced square trinomials with real coefficients; real solutions; complex solutions; dynamic model LATEX<\/p>\n<a href=\"https:\/\/philosophy.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"<p>Aslanbek Khamidovitch Naziev Ryazan State University named for S. A. Esenin, Ryazan \u2013 Ryazan (Russian Federation) Ryazan Institute for Education Development \u2013 Ryazan (Russian Federation) https:\/\/doi.org\/10.53656\/math2022-6-1-com Abstract. Many people think that inequalities cannot be considered over the field\u00a0 C of complex numbers. And really, on C does not possess an order to make it an [&hellip;]<\/p>","protected":false},"author":124332423426818,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":{"subtitle":"","format":"standard","video":"","gallery":"","source_name":"","source_url":"","via_name":"","via_url":"","override_template":"0","override":[{"single_blog_custom":"","parallax":"0","fullscreen":"0","sidebar":"","second_sidebar":"","sticky_sidebar":"0","share_position":"","share_float_style":"","show_share_counter":"0","show_view_counter":"0","show_featured":"0","show_post_meta":"0","show_post_author":"0","show_post_author_image":"0","show_post_date":"0","post_date_format":"","post_date_format_custom":"","show_post_category":"0","show_post_reading_time":"0","post_reading_time_wpm":"","show_post_tag":"0","show_prev_next_post":"0","show_popup_post":"0","number_popup_post":"1","show_author_box":"0","show_post_related":"0","show_inline_post_related":"0"}],"override_image_size":"0","image_override":[{"single_post_thumbnail_size":"","single_post_gallery_size":""}],"trending_post":"0","trending_post_position":"","trending_post_label":""},"jnews_primary_category":{"id":""}},"categories":[1],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Complex Solutions to Quadratic Inequalities and Their Modeling by Means of LATEX - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Complex Solutions to Quadratic Inequalities and Their Modeling by Means of LATEX - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"Aslanbek Khamidovitch Naziev Ryazan State University named for S. A. Esenin, Ryazan \u2013 Ryazan (Russian Federation) Ryazan Institute for Education Development \u2013 Ryazan (Russian Federation) https:\/\/doi.org\/10.53656\/math2022-6-1-com Abstract. Many people think that inequalities cannot be considered over the field\u00a0 C of complex numbers. 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A. Esenin, Ryazan \u2013 Ryazan (Russian Federation) Ryazan Institute for Education Development \u2013 Ryazan (Russian Federation) https:\/\/doi.org\/10.53656\/math2022-6-1-com Abstract. Many people think that inequalities cannot be considered over the field\u00a0 C of complex numbers. And really, on C does not possess an order to make it an [&hellip;]","og_url":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/","og_site_name":"\u0410\u0437-\u0431\u0443\u043a\u0438","article_publisher":"https:\/\/www.facebook.com\/Azbuki55\/","article_published_time":"2022-12-24T14:24:21+00:00","article_modified_time":"2025-09-16T14:09:35+00:00","author":"v.genkov@azbuki.bg","twitter_card":"summary_large_image","twitter_misc":{"Written by":"v.genkov@azbuki.bg","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/#article","isPartOf":{"@id":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/"},"author":{"name":"v.genkov@azbuki.bg","@id":"https:\/\/azbuki.bg\/#\/schema\/person\/92cc38d6a11fb032bf6299efd22a71c5"},"headline":"Complex Solutions to Quadratic Inequalities and Their Modeling by Means of LATEX","datePublished":"2022-12-24T14:24:21+00:00","dateModified":"2025-09-16T14:09:35+00:00","mainEntityOfPage":{"@id":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/"},"wordCount":233,"publisher":{"@id":"https:\/\/azbuki.bg\/#organization"},"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/","url":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/complex-solutions-to-quadratic-inequalities-and-their-modeling-by-means-of-latex\/","name":"Complex Solutions to Quadratic Inequalities and Their Modeling by Means of LATEX - 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