{"id":181527,"date":"2025-01-11T02:09:59","date_gmt":"2025-01-11T02:09:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=181527"},"modified":"2025-01-11T02:10:02","modified_gmt":"2025-01-11T02:10:02","slug":"1-convert-148-pounds-to-kilograms-round-your-answer-to-the-nearest-tenth-kg-2-in-z3i","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/11\/1-convert-148-pounds-to-kilograms-round-your-answer-to-the-nearest-tenth-kg-2-in-z3i\/","title":{"rendered":"1. Convert 148 pounds to kilograms Round your answer to the nearest tenth. Kg 2. In Z3i)"},"content":{"rendered":"\n
    \n
  1. Convert 148 pounds to kilograms Round your answer to the nearest tenth. Kg<\/li>\n\n\n\n
  2. In Z3i), a. Write the additive inverse of 2 + i. b. Write the multiplicative inverse of (21) (1 + i)2 in the form a + bi.<\/li>\n<\/ol>\n\n\n\n

    the correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

    1. Convert 148 pounds to kilograms:<\/h3>\n\n\n\n

    To convert pounds to kilograms, use the conversion factor 1\u2009pound=0.453592\u2009kilograms1 \\, \\text{pound} = 0.453592 \\, \\text{kilograms}. 148\u2009pounds\u00d70.453592\u2009kg\/pound=67.131024\u2009kg148 \\, \\text{pounds} \\times 0.453592 \\, \\text{kg\/pound} = 67.131024 \\, \\text{kg}<\/p>\n\n\n\n

    Rounded to the nearest tenth: 67.1\u2009kg67.1 \\, \\text{kg}<\/p>\n\n\n\n

    Answer:<\/strong> 67.1\u2009kg67.1 \\, \\text{kg}<\/p>\n\n\n\n

    \n\n\n\n

    2. Z3i)<\/h3>\n\n\n\n

    a. Write the additive inverse of 2+i2 + i:<\/h4>\n\n\n\n

    The additive inverse of a complex number a+bia + bi is \u2212a\u2212bi-a – bi. For 2+i2 + i: Additive inverse=\u22122\u2212i\\text{Additive inverse} = -2 – i<\/p>\n\n\n\n

    Answer:<\/strong> \u22122\u2212i-2 – i<\/p>\n\n\n\n

    b. Write the multiplicative inverse of (2+i)2(2 + i)^2 in the form a+bia + bi:<\/h4>\n\n\n\n
      \n
    1. Expand (2+i)2(2 + i)^2:<\/strong><\/li>\n<\/ol>\n\n\n\n

      (2+i)2=(2+i)(2+i)=4+4i+i2(2 + i)^2 = (2 + i)(2 + i) = 4 + 4i + i^2<\/p>\n\n\n\n

      Since i2=\u22121i^2 = -1: (2+i)2=4+4i\u22121=3+4i(2 + i)^2 = 4 + 4i – 1 = 3 + 4i<\/p>\n\n\n\n

        \n
      1. Find the multiplicative inverse of 3+4i3 + 4i:<\/strong> The multiplicative inverse of a complex number z=a+biz = a + bi is given by:<\/li>\n<\/ol>\n\n\n\n

        1z=conjugate of z\u2223z\u22232\\frac{1}{z} = \\frac{\\text{conjugate of } z}{\\lvert z \\rvert^2}<\/p>\n\n\n\n

        For z=3+4iz = 3 + 4i, the conjugate is 3\u22124i3 – 4i, and the magnitude squared is: \u2223z\u22232=32+42=9+16=25\\lvert z \\rvert^2 = 3^2 + 4^2 = 9 + 16 = 25<\/p>\n\n\n\n

        Thus: 13+4i=3\u22124i25=325\u2212425i\\frac{1}{3 + 4i} = \\frac{3 – 4i}{25} = \\frac{3}{25} – \\frac{4}{25}i Multiplicative inverse=0.12\u22120.16i\\text{Multiplicative inverse} = 0.12 – 0.16i<\/p>\n\n\n\n

        Answer:<\/strong> 0.12\u22120.16i0.12 – 0.16i<\/p>\n\n\n\n

        \n\n\n\n

        Explanation:<\/h3>\n\n\n\n

        Complex numbers combine a real part and an imaginary part in the form a+bia + bi. To solve the problems in Z3i, understanding key properties like the additive and multiplicative inverses is crucial.<\/p>\n\n\n\n

        The additive inverse<\/strong> of a complex number is the number that, when added to the original number, gives zero. For example, the additive inverse of 2+i2 + i is \u22122\u2212i-2 – i because: (2+i)+(\u22122\u2212i)=0(2 + i) + (-2 – i) = 0<\/p>\n\n\n\n

        The multiplicative inverse<\/strong> involves finding a number that, when multiplied with the original, gives 11. For z=3+4iz = 3 + 4i, its multiplicative inverse is: 1z=conjugate of z\u2223z\u22232\\frac{1}{z} = \\frac{\\text{conjugate of } z}{\\lvert z \\rvert^2}<\/p>\n\n\n\n

        Here, \u2223z\u22232=25\\lvert z \\rvert^2 = 25 is derived from the Pythagorean theorem applied to a=3a = 3 and b=4b = 4. The conjugate, 3\u22124i3 – 4i, ensures the imaginary part cancels when dividing. Simplifying yields: 325\u2212425i\\frac{3}{25} – \\frac{4}{25}i<\/p>\n\n\n\n

        Understanding these inverses helps in fields like signal processing or solving differential equations, where complex numbers play a key role.<\/p>\n","protected":false},"excerpt":{"rendered":"

        the correct answer and explanation is: 1. Convert 148 pounds to kilograms: To convert pounds to kilograms, use the conversion factor 1\u2009pound=0.453592\u2009kilograms1 \\, \\text{pound} = 0.453592 \\, \\text{kilograms}. 148\u2009pounds\u00d70.453592\u2009kg\/pound=67.131024\u2009kg148 \\, \\text{pounds} \\times 0.453592 \\, \\text{kg\/pound} = 67.131024 \\, \\text{kg} Rounded to the nearest tenth: 67.1\u2009kg67.1 \\, \\text{kg} Answer: 67.1\u2009kg67.1 \\, \\text{kg} 2. Z3i) a. Write […]<\/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-181527","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181527","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=181527"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181527\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=181527"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=181527"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=181527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}