{"id":455,"date":"2015-10-26T19:19:30","date_gmt":"2015-10-26T19:19:30","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=455"},"modified":"2017-03-31T18:26:40","modified_gmt":"2017-03-31T18:26:40","slug":"add-and-subtract-complex-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/add-and-subtract-complex-numbers\/","title":{"raw":"Add and subtract complex numbers","rendered":"Add and subtract complex numbers"},"content":{"raw":"

Just as with real numbers, we can perform arithmetic operations on complex numbers. To add or subtract complex numbers, we combine the real parts and combine the imaginary parts.<\/p>\r\n\r\n

\r\n

A General Note: Addition and Subtraction of Complex Numbers<\/h3>\r\n

Adding complex numbers:<\/p>\r\n\r\n

[latex]\\left(a+bi\\right)+\\left(c+di\\right)=\\left(a+c\\right)+\\left(b+d\\right)i[\/latex]<\/div>\r\n

Subtracting complex numbers:<\/p>\r\n\r\n

[latex]\\left(a+bi\\right)-\\left(c+di\\right)=\\left(a-c\\right)+\\left(b-d\\right)i[\/latex]<\/div>\r\n<\/div>\r\n
\r\n

How To: Given two complex numbers, find the sum or difference.<\/h3>\r\n
    \r\n \t
  1. Identify the real and imaginary parts of each number.<\/li>\r\n \t
  2. Add or subtract the real parts.<\/li>\r\n \t
  3. Add or subtract the imaginary parts.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    \r\n
    \r\n
    \r\n

    Example 3: Adding Complex Numbers<\/h3>\r\n

    Add [latex]3 - 4i[\/latex] and [latex]2+5i[\/latex].<\/p>\r\n\r\n<\/div>\r\n

    \r\n

    Solution<\/h3>\r\n

    We add the real parts and add the imaginary parts.<\/p>\r\n\r\n

    [latex]\\begin{cases}\\left(a+bi\\right)+\\left(c+di\\right)=\\left(a+c\\right)+\\left(b+d\\right)i\\hfill \\\\ \\left(3 - 4i\\right)+\\left(2+5i\\right)=\\left(3+2\\right)+\\left(-4+5\\right)i\\hfill \\\\ \\text{ }=5+i\\hfill \\end{cases}[\/latex]<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
    \r\n

    Try It 3<\/h3>\r\n

    Subtract [latex]2+5i[\/latex] from [latex]3 - 4i[\/latex].<\/p>\r\nSolution<\/a>\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/SGhTjioGqqA","rendered":"

    Just as with real numbers, we can perform arithmetic operations on complex numbers. To add or subtract complex numbers, we combine the real parts and combine the imaginary parts.<\/p>\n

    \n

    A General Note: Addition and Subtraction of Complex Numbers<\/h3>\n

    Adding complex numbers:<\/p>\n

    [latex]\\left(a+bi\\right)+\\left(c+di\\right)=\\left(a+c\\right)+\\left(b+d\\right)i[\/latex]<\/div>\n

    Subtracting complex numbers:<\/p>\n

    [latex]\\left(a+bi\\right)-\\left(c+di\\right)=\\left(a-c\\right)+\\left(b-d\\right)i[\/latex]<\/div>\n<\/div>\n
    \n

    How To: Given two complex numbers, find the sum or difference.<\/h3>\n
      \n
    1. Identify the real and imaginary parts of each number.<\/li>\n
    2. Add or subtract the real parts.<\/li>\n
    3. Add or subtract the imaginary parts.<\/li>\n<\/ol>\n<\/div>\n
      \n
      \n
      \n

      Example 3: Adding Complex Numbers<\/h3>\n

      Add [latex]3 - 4i[\/latex] and [latex]2+5i[\/latex].<\/p>\n<\/div>\n

      \n

      Solution<\/h3>\n

      We add the real parts and add the imaginary parts.<\/p>\n

      [latex]\\begin{cases}\\left(a+bi\\right)+\\left(c+di\\right)=\\left(a+c\\right)+\\left(b+d\\right)i\\hfill \\\\ \\left(3 - 4i\\right)+\\left(2+5i\\right)=\\left(3+2\\right)+\\left(-4+5\\right)i\\hfill \\\\ \\text{ }=5+i\\hfill \\end{cases}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n

      Try It 3<\/h3>\n

      Subtract [latex]2+5i[\/latex] from [latex]3 - 4i[\/latex].<\/p>\n

      Solution<\/a><\/p>\n<\/div>\n