{"id":17446,"date":"2025-06-12T12:31:51","date_gmt":"2025-06-12T12:31:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=17446"},"modified":"2025-06-12T12:32:13","modified_gmt":"2025-06-12T12:32:13","slug":"which-subtraction-expression-has-the-difference-1-4i","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-subtraction-expression-has-the-difference-1-4i\/","title":{"rendered":"Which subtraction expression has the difference 1 + 4i"},"content":{"rendered":"\n

Which subtraction expression has the difference 1 + 4i?<\/p>\n\n\n\n

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

To find which subtraction expression has the difference 1 + 4i<\/strong>, we need to recall how subtraction works with complex numbers.<\/p>\n\n\n\n

Step 1: Understanding complex number subtraction<\/h3>\n\n\n\n

Complex numbers are in the form a + bi<\/strong>, where a<\/strong> is the real part and b<\/strong> is the imaginary part.<\/p>\n\n\n\n

To subtract complex numbers:
(a + bi) \u2212 (c + di) = (a \u2212 c) + (b \u2212 d)i<\/strong><\/p>\n\n\n\n

We are told the result<\/strong> (difference) is:
1 + 4i<\/strong><\/p>\n\n\n\n

So, we are looking for complex numbers A and B such that:
A \u2212 B = 1 + 4i<\/strong><\/p>\n\n\n\n

Let\u2019s reverse-engineer the problem. Suppose:
A = x + yi<\/strong>
B = m + ni<\/strong>
Then:
(x + yi) \u2212 (m + ni) = (x \u2212 m) + (y \u2212 n)i = 1 + 4i<\/strong><\/p>\n\n\n\n

From this, we get two equations:<\/p>\n\n\n\n

    \n
  • x \u2212 m = 1<\/strong><\/li>\n\n\n\n
  • y \u2212 n = 4<\/strong><\/li>\n<\/ul>\n\n\n\n

    This means we can choose any pair of complex numbers that differ by 1 in the real part and 4 in the imaginary part.<\/p>\n\n\n\n

    Example (Correct Answer):<\/h3>\n\n\n\n

    Let\u2019s choose:<\/p>\n\n\n\n

      \n
    • A = 3 + 6i<\/strong><\/li>\n\n\n\n
    • B = 2 + 2i<\/strong><\/li>\n<\/ul>\n\n\n\n

      Now check:
      (3 + 6i) \u2212 (2 + 2i) = (3 \u2212 2) + (6 \u2212 2)i = 1 + 4i<\/strong><\/p>\n\n\n\n

      \u2705 This is the correct answer.<\/p>\n\n\n\n

      \n\n\n\n

      Explanation (300 words):<\/h3>\n\n\n\n

      Subtraction of complex numbers works similarly to subtracting binomials. Each complex number has two parts: a real part and an imaginary part. The real and imaginary components are subtracted separately.<\/p>\n\n\n\n

      Given the difference 1 + 4i<\/strong>, we want to identify a subtraction expression that results in this. Think of subtraction as \u201cwhat must be taken away from the first number to leave 1 + 4i?\u201d In algebraic terms, if we have A \u2212 B = 1 + 4i<\/strong>, then the difference between the real parts of A and B must be 1, and the difference between their imaginary parts must be 4.<\/p>\n\n\n\n

      Using this logic, let\u2019s consider two complex numbers:
      A = 3 + 6i<\/strong>
      B = 2 + 2i<\/strong><\/p>\n\n\n\n

      Subtracting B from A:
      (3 \u2212 2) + (6 \u2212 2)i = 1 + 4i<\/strong><\/p>\n\n\n\n

      This matches the target result. Therefore, the subtraction expression (3 + 6i) \u2212 (2 + 2i)<\/strong> is a correct answer.<\/p>\n\n\n\n

      This concept shows how complex number subtraction is straightforward when treated systematically. We just work with the real and imaginary components separately, and by setting up basic equations, we can find numerous pairs of complex numbers whose difference gives any desired result.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Which subtraction expression has the difference 1 + 4i? The correct answer and explanation is: To find which subtraction expression has the difference 1 + 4i, we need to recall how subtraction works with complex numbers. Step 1: Understanding complex number subtraction Complex numbers are in the form a + bi, where a is the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-17446","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=17446"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17446\/revisions"}],"predecessor-version":[{"id":17448,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17446\/revisions\/17448"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=17446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=17446"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=17446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}