{"id":861,"date":"2024-09-22T10:56:22","date_gmt":"2024-09-22T02:56:22","guid":{"rendered":"https:\/\/www.math.ntnu.edu.tw\/merc\/?page_id=861"},"modified":"2025-10-16T15:39:12","modified_gmt":"2025-10-16T07:39:12","slug":"%e8%a4%87%e6%95%b8%e6%a5%b5%e5%bc%8f%e7%9a%84%e4%b9%98%e6%b3%95","status":"publish","type":"page","link":"https:\/\/www.math.ntnu.edu.tw\/merc\/animated_math\/%e8%a4%87%e6%95%b8%e6%a5%b5%e5%bc%8f%e7%9a%84%e4%b9%98%e6%b3%95\/","title":{"rendered":"\u8907\u6578\u6975\u5f0f\u7684\u4e58\u6cd5"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"861\" class=\"elementor elementor-861\">\n\t\t\t\t<div class=\"elementor-element elementor-element-351bb8b7 e-flex e-con-boxed e-con e-parent\" data-id=\"351bb8b7\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7c8d56cc elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"7c8d56cc\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;bounceIn&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u821e\u52d5\u6578\u5b78<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5c69ade1 e-flex e-con-boxed e-con e-parent\" data-id=\"5c69ade1\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-589bddd7 elementor-widget elementor-widget-heading\" data-id=\"589bddd7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u8907\u6578\u6975\u5f0f\u7684\u4e58\u6cd5<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1091112 e-flex e-con-boxed e-con e-parent\" data-id=\"1091112\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4c39964b elementor-widget elementor-widget-video\" data-id=\"4c39964b\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/workshop\/animated_math\/media\/multiplication.mp4\" autoplay=\"\" loop=\"\" controls=\"\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4ee7d3f0 e-flex e-con-boxed e-con e-parent\" data-id=\"4ee7d3f0\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4918ec73 elementor-widget elementor-widget-text-editor\" data-id=\"4918ec73\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\u63a2\u7d22 $w=(4+3i) \\cdot z$ \u7684\u7d55\u5c0d\u503c\u8207\u8f3b\u89d2\uff1a\n<div class=\"row\">\n<div class=\"col\">\u5982\u53f3\u5716\uff0c\u8a2d $A(z)$\u3001$B(iz)$\uff0c\u4e14\u4ee4 $Arg(z)=\\alpha$\uff0c$Arg(4+3i)=\\theta$\n\uff0c\u6839\u64da\u5206\u914d\u5f8b $(4+3i)z=(4z)+3(iz)$\uff0c\u5982\u5716\uff0c\n\u63cf\u7e6a\u51fa $P(4z)$\u3001$Q(3(iz))$\u3001$R(w)$\uff0c\n\u56e0\u70ba $z$ \u7e5e\u539f\u9ede\u9006\u6642\u91dd\u65cb\u8f49 $90^{\\circ}$ \u53ef\u5f97 $iz$\uff0c\n\u6240\u4ee5$\\angle AOB=90^{\\circ}$\uff0c\u6545 $OPRQ$ \u70ba\u77e9\u5f62\u3002\n\u56e0\u70ba $\\overline{OP}=4|z|$\uff0c $\\overline{OQ}=3|iz|=3|z|$\uff0c\u6240\u4ee5\n$\\frac{\\overline{OP}}{\\overline{OQ}}=\\frac{4}{3}$\u3002\n<ul>\n \t<li>\u8003\u616e(4+3i)z\u7684\u7d55\u5c0d\u503c\uff1a\n$$ \\begin{array}{rl}\n|(4+3i)z| &amp; =\\overline{OR}=\\sqrt{\\overline{OP}^2+\\overline{OQ}^2} \\\\\n&amp; =\\sqrt{(4|z|)^2+(3|z|)^2} \\\\\n&amp; =\\sqrt{4^2+3^2}|z|=|4+3i||z|.\n\\end{array}\n$$<\/li>\n \t<li>\u8003\u616e((4+3i)z)\u7684\u8f3b\u89d2\uff1a\n\u56e0\u70ba $\\frac{\\overline{OP}}{\\overline{OQ}}=\\frac{4}{3}$\uff0c\u6240\u4ee5\n$\\angle POR= Arg(4+3i)=\\theta$\uff0c\u6545 $Arg((4+3i)z)=\n\\alpha+\\theta=Arg(z)+Arg(4+3i)$\uff0c\n\u56e0\u6b64\u5f97\u5230\u4ee5\u4e0b\u7d50\u679c\uff1a\n<b>$|(4+3i)z|=|4+3i||z|$\uff0c\n$(4+3i)z$ \u7684\u8f3b\u89d2\u53ef\u53d6\u70ba $(4+3i)$\n\u8207 $z$ \u7684\u8f3b\u89d2\u4e4b\u548c\u3002<\/b><\/li>\n<\/ul>\n<\/div>\n<div class=\"col\"><img decoding=\"async\" style=\"max-width: 100%;\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/workshop\/animated_math\/images\/multiplication_pic.png\" \/><\/div>\n<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2e1125f1 e-flex e-con-boxed e-con e-parent\" data-id=\"2e1125f1\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-26756781 elementor-widget elementor-widget-text-editor\" data-id=\"26756781\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"color: #306f7f;\"><a href=\"https:\/\/cantor.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u8907\u6578\u6975\u5f0f\u7684\u4e58\u6cd5(\u5b78\u7fd2\u55ae).pdf\" target=\"_blank\" rel=\"noopener\">\u8907\u6578\u6975\u5f0f\u7684\u4e58\u6cd5(\u5b78\u7fd2\u55ae)<\/a><\/p>\n\n\n<hr style=\"margin-bottom: 20px;\" \/>\n<p style=\"color: #306f7f;\">\u88fd\u4f5c\u4eba\uff1a\u6797\u4fe1\u5b89<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u821e\u52d5\u6578\u5b78 \u8907\u6578\u6975\u5f0f\u7684\u4e58\u6cd5 https:\/\/cantor.math.ntnu.edu.tw\/workshop\/a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":193,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ocean_post_layout":"full-width","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-861","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/861","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/comments?post=861"}],"version-history":[{"count":7,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/861\/revisions"}],"predecessor-version":[{"id":868,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/861\/revisions\/868"}],"up":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/193"}],"wp:attachment":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/media?parent=861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}