{"id":18444,"date":"2026-05-03T04:34:34","date_gmt":"2026-05-02T22:34:34","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/complex-number-algebra-15\/"},"modified":"2026-05-03T04:34:34","modified_gmt":"2026-05-02T22:34:34","slug":"complex-number-algebra-15","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/complex-number-algebra-15\/","title":{"rendered":"Complex Number Algebra 15"},"content":{"rendered":"<p>For z=3+-2i, find z\u00b7conjugate(z).<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>5<\/li>\n<li>6<\/li>\n<li>13<\/li>\n<li>-4<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705,2733],"subject":[1425],"education_level":[1896],"class_list":["post-18444","mcq","type-mcq","status-publish","hentry","topic-algebra","topic-complex-numbers","subject-mathematics","education_level-hsc"],"mcq_note":"For a complex number z = a + bi, multiplying by its conjugate gives z\u00b7conjugate(z) = a\u00b2 + b\u00b2. This is the square of the modulus, so it is always non-negative. Here a = 3 and b = -2. Therefore z\u00b7conjugate(z) = (3)\u00b2 + (-2)\u00b2 = 9 + 4 = 13. So the correct answer is 13.","mcq_options":[{"right":"no","answer":"5"},{"right":"no","answer":"6"},{"right":"yes","answer":"13"},{"right":"no","answer":"-4"}],"multi_answers":"no","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"},{"id":2733,"title":"Complex Numbers","slug":"complex-numbers"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/18444","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=18444"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=18444"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=18444"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=18444"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=18444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}