{"id":192958,"date":"2025-02-18T13:18:39","date_gmt":"2025-02-18T13:18:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=192958"},"modified":"2025-02-18T13:18:59","modified_gmt":"2025-02-18T13:18:59","slug":"vanessa-invested-2500-into-an-account-that-will-increase-in-value-by-3-5-each-year","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/18\/vanessa-invested-2500-into-an-account-that-will-increase-in-value-by-3-5-each-year\/","title":{"rendered":"Vanessa invested $2,500 into an account that will increase in value by 3.5% each year"},"content":{"rendered":"\n
    \n
  1. Vanessa invested $2,500 into an account that will increase in value by 3.5% each year. What is the rate in this problem?” Your answer<\/li>\n\n\n\n
  2. What is the additive identity of the complex number 14+5i?<\/li>\n<\/ol>\n\n\n\n

    The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

      \n
    1. The rate in the problem is 3.5%<\/strong>. This is the percentage by which Vanessa’s investment increases each year. The rate refers to the growth or increase in value relative to the initial amount, expressed as a percentage.<\/li>\n\n\n\n
    2. The additive identity<\/strong> of a complex number is the number that, when added to any complex number, does not change the value of that complex number. In the case of the complex number 14 + 5i<\/strong>, the additive identity is 0 + 0i<\/strong>, or simply 0<\/strong>.<\/li>\n<\/ol>\n\n\n\n

      Here\u2019s why:<\/p>\n\n\n\n

      In mathematics, the additive identity<\/strong> is the element that leaves other elements unchanged when added to them. For real numbers, the additive identity is 0<\/strong>, because adding 0 to any real number doesn\u2019t change its value (e.g., 5 + 0 = 5). Similarly, in the set of complex numbers, the additive identity is the complex number 0 + 0i<\/strong>, which is simply the complex number 0<\/strong>.<\/p>\n\n\n\n

      A complex number is of the form a + bi<\/strong>, where a<\/strong> is the real part and bi<\/strong> is the imaginary part. The number 14 + 5i<\/strong> has a real part of 14<\/strong> and an imaginary part of 5i<\/strong>. To add two complex numbers, you add the real parts together and the imaginary parts together. So, for example:<\/p>\n\n\n\n

      [
      (14 + 5i) + (0 + 0i) = 14 + 5i
      ]<\/p>\n\n\n\n

      This shows that adding the additive identity (0 + 0i) to the complex number (14 + 5i) leaves it unchanged.<\/p>\n\n\n\n

      In conclusion, the additive identity of the complex number 14 + 5i<\/strong> is 0<\/strong> or 0 + 0i<\/strong>. This is because adding 0 + 0i<\/strong> to any complex number will not alter its value, just as adding 0<\/strong> to any real number does not change its value.<\/p>\n","protected":false},"excerpt":{"rendered":"

      The Correct Answer and Explanation is : Here\u2019s why: In mathematics, the additive identity is the element that leaves other elements unchanged when added to them. For real numbers, the additive identity is 0, because adding 0 to any real number doesn\u2019t change its value (e.g., 5 + 0 = 5). Similarly, in the set […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-192958","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192958","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=192958"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192958\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=192958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=192958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=192958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}