Dividing Complex Numbers by Complex Numbers<\/p>\n
Addition and multiplication of complex numbers is straightforward. If you divide by a real number it is easy: divide real and non real parts by the number, for example: (2 + 6i)\/2 = 1 + 3i.<\/p>\n
Division by a non-real number takes a little more work. The trick is to turn division into multiplication, using the complex conjugate.<\/p>\n
Example: (2 + 3i) \/ (1 – i)<\/p>\n
Multiply numerator and denominator by the complex conjugate of 1 – i, which is 1 + i:<\/p>\n
(2 + 3i) x (1 + i ) = 2 – 3 + 3i + i = -1 + 4i<\/p>\n
(1 – i) x (1 + i) = 1 – i + i + 1 = 2<\/p>\n
Solution: (-1 + 4i)\/2 = -1\/2 + 2i<\/p>\n
In the following problems, do the division.<\/p>\n
1. 1 \/ i<\/p>\n
(1 divided by i).<\/p>\n
2. (2 + 3i)\/i<\/p>\n
3. (1 + i) \/ (1 – i)<\/p>\n
4. i \/ (1 – i)<\/p>\n
5. (3 – 2i) \/ (3 + 2i)<\/p>\n","protected":false},"excerpt":{"rendered":"
Dividing Complex Numbers by Complex Numbers Addition and multiplication of complex numbers is straightforward. If you divide by a real number it is easy: divide real and non real parts by the number, for example: (2 + 6i)\/2 = 1 + 3i. Division by a non-real number takes a little more work. The trick is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-97","post","type-post","status-publish","format-standard","hentry","category-complex-numbers"],"_links":{"self":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/97","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=97"}],"version-history":[{"count":2,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/97\/revisions"}],"predecessor-version":[{"id":112,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/97\/revisions\/112"}],"wp:attachment":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=97"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=97"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=97"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}