{"id":3288,"date":"2012-11-17T14:21:00","date_gmt":"2012-11-17T05:21:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3288"},"modified":"2021-09-01T20:27:13","modified_gmt":"2021-09-01T11:27:13","slug":"%eb%b3%b5%ec%86%8c%ed%95%b4%ec%84%9d%ed%95%992","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2012\/11\/17\/%eb%b3%b5%ec%86%8c%ed%95%b4%ec%84%9d%ed%95%992\/","title":{"rendered":"\ubcf5\uc18c\ud574\uc11d\ud5592"},"content":{"rendered":"
\n

\uacf5\uc9c0\uc0ac\ud56d<\/h2>\n<\/div>\n
\n

\uc9c4\ub3c4<\/h2>\n<\/div>\n
\n

\uc219\uc81c\uc5d0 \ub300\ud55c \uc9c8\ubb38\uacfc \ub2f5<\/h2>\n<\/div>\n
\n

[wiki:2k12FallCpxAnalysisTransl \ubc88\uc5edpage]<\/h2>\n
\n

\uc218\ud559\uacfc 2009160192 \ud5c8\uc815\ud638 <\/p>\n

Complex Analysis (Lipman Bers) <\/p>\n

One of the first purely mathematical problems ever considered was the solution of quadratic equations. \uc774\ucc28\ubc29\uc815\uc2dd\uc758 \ud574\ub97c \uad6c\ud558\ub294 \uac83\uc740 \uc21c\uc218 \uc218\ud559 \uc5ed\uc0ac\uc5d0 \uc788\uc5b4\uc11c \uac00\uc7a5 \uc624\ub798\ub41c \ubb38\uc81c \uc911 \ud558\ub098\uc600\ub2e4. The technique of solving such equations was discovered in ancient times in Babylonia; it is essentially the same technique as is taught today in high schools. \uadf8\ub7ec\ud55c \ubc29\uc815\uc2dd\uc758 \ud574\ub97c \uad6c\ud558\ub294 \uae30\ubc95\uc740 \uace0\ub300 \ubc14\ube4c\ub85c\ub2c8\uc544\uc5d0\uc11c \ubc1c\uacac\ub418\uc5c8\ub2e4. \uadf8\ub9ac\uace0 \uadf8\uac83\uc740 \uc624\ub298\ub0a0 \uace0\ub4f1\ud559\uad50\uc5d0\uc11c \uc6b0\ub9ac\uac00 \ubc30\uc6b0\ub294 \uac83\uacfc \ubcf8\uc9c8\uc801\uc73c\ub85c \uac19\ub2e4. To find a number \\[ x \\] such that \\[ x^2 – 2x – 15 = 0 \\] ,we write the equation in the form \\[ x^2 – 2x + 1 – 16 = 0 \\] and conclude that \\[ (x – 1)^2 = 16 \\] which is the same as \\[ (x – 1)^2 = 16 \\] so that either \\[ x – 1 = 4 \\] or \\[ x – 1 = -4 \\] . Hence either \\[ x = 5 \\] or \\[ x = -3 \\] . \\[ x^2 – 2x – 15 = 0 \\] \ub97c \ub9cc\uc871\ud558\ub294 \uc218 \\[ x \\] \ub97c \ucc3e\uae30 \uc704\ud558\uc5ec \uc6b0\ub9ac\ub294 \uc8fc\uc5b4\uc9c4 \ubc29\uc815\uc2dd\uc744 \\[ x^2 – 2x + 1 – 16 = 0 \\] \ub85c \uace0\uccd0\uc4f8 \uc218 \uc788\uace0 \uc774\uac83\uc740 \ub2e4\uc2dc \\[ (x – 1)^2 = 16 \\] \uacfc \uac19\ub2e4. \ub530\ub77c\uc11c \\[ x – 1 = 4 \\] \uc774\uac70\ub098 \\[ x – 1 = -4 \\] \uc774\uac8c \ub41c\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\[ x = 5 \\] \ub610\ub294 \\[ x = -3 \\] \uc774\ub2e4. But there are quadratic equations for which this method of “completing the square” fails. \uadf8\ub7ec\ub098 \uc774\ub7ec\ud55c “\uc644\uc804\uc81c\uacf1” \ubc29\uc2dd\uc744 \uc4f8\uc218 \uc5c6\ub294 \uc774\ucc28\ubc29\uc815\uc2dd\uc774 \uc874\uc7ac\ud55c\ub2e4. For instance, if we want to solve the equation \\[ x^2 – 2x + 17 = 0 \\] , we are led to finding a number \\[ x \\] such that \\[ (x – 1)^2 = -16 \\] , and this seems impossible. \uc608\ub97c \ub4e4\uc5b4, \uc6b0\ub9ac\uac00 \ub9cc\uc57d \\[ x^2 – 2x + 17 = 0 \\] \uacfc \uac19\uc740 \ubc29\uc815\uc2dd\uc744 \ud480\uace0\uc790 \ud55c\ub2e4\uba74 \uadf8\uac83\uc740 \\[ (x – 1)^2 = -16 \\] \ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \\[ x \\] \ub97c \ucc3e\ub294 \uac83\uacfc \uac19\uace0 \uc774\uac83\uc740 \ubd88\uac00\ub2a5 \ud574 \ubcf4\uc778\ub2e4. The square of a number is never negative. \uc5b4\ub5a4 \uc2e4\uc218\uc758 \uc81c\uacf1\uc740 \uc808\ub300 \uc74c\uc218\uac00 \ub420 \uc218 \uc5c6\ub2e4. As a matter of fact, there was no need to consider a somewhat elaborate example. \uc0ac\uc2e4 \uc704\uc640 \uac19\uc774 \ubcf5\uc7a1\ud55c \ubc29\uc815\uc2dd\uc744 \uc608\ub85c \ub4e4 \ud544\uc694\ub294 \uc5c6\ub2e4. The simple quadratic equation \\[ x^2 = -1 \\] clearly has no solutions. \uac04\ub2e8\ud55c \uc774\ucc28\ubc29\uc815\uc2dd \\[ x^2 = -1 \\] \uc740 \ubd84\uba85\ud788 \ud574\ub97c \uac16\uc9c0 \uc54a\ub294\ub2e4. <\/p>\n

During the Renaissance an Italian mathematician had the brilliant and somewhat crazy idea of imagining what whould have happend if there were a number whose square is -1. \ub974\ub124\uc0c1\uc2a4 \uc2dc\ub300\uc5d0 \uc774\ud0c8\ub9ac\uc544\uc758 \ud55c \uc218\ud559\uc790\ub294 \uc81c\uacf1\ud574\uc11c \\[ -1 \\] \uc774 \ub418\ub294 \uc218\uac00 \uc874\uc7ac\ud55c\ub2e4\uba74 \uc5b4\ub5a4 \uc77c\uc774 \ubc8c\uc5b4\uc9c8 \uac83\uc778 \uac00\uc640 \uac19\uc774 \ucc9c\uc7ac\uc801\uc774\uba74\uc11c\ub3c4 \ub9d0\ub3c4 \uc548\ub418\ub294 \uc0dd\uac01\uc744 \ud558\uac8c \ub418\uc5c8\ub2e4. This number is denoted today by \\[ i \\] and is called the “imaginary” unit. \uc774 \uc22b\uc790\ub294 \uc624\ub298\ub0a0 \\[ i \\] \ub85c \uc4f0\uc5ec\uc9c0\uba70 “imaginary” unit \uc774\ub77c\uace0 \ubd88\ub9ac\uc6b4\ub2e4. The agreement, originate during the Renaissance and still used today, is that we compute with \\[ i \\] as if it were an ordinary number, but whenever the term \\[ i^2 = i X i \\] appears, it is replaced by \\[ -1 \\] . \uc774 \\[ i \\] \ub97c \ub9c8\uce58 \uc2e4\uc218\ucc98\ub7fc \uacc4\uc0b0\uc744 \ud558\ub294 \ubc29\uc2dd\uc740 \ub974\ub124\uc0c1\uc2a4 \uc2dc\ub300\ubd80\ud130 \uc2dc\uc791\ud574 \uc654\uc73c\uba70 \uc544\uc9c1\ub3c4 \uc4f0\uc5ec\uc9c4\ub2e4. \ud55c\ud3b8 \\[ i^2 = i X i \\] \uc740 \\[ -1 \\] \ub85c \ub300\uc2e0 \uc4f8 \uc218 \uc788\ub2e4. <\/p>\n<\/div>\n<\/div>\n

\n

Q+A<\/h2>\n
\n
\n

Q: <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\uacf5\uc9c0\uc0ac\ud56d \uc9c4\ub3c4 \uc219\uc81c\uc5d0 \ub300\ud55c \uc9c8\ubb38\uacfc \ub2f5 [wiki:2k12FallCpxAnalysisTransl \ubc88\uc5edpage] \uc218\ud559\uacfc 2009160192 \ud5c8\uc815\ud638 Complex Analysis (Lipman Bers) One of the first purely mathematical problems ever considered was the solution of quadratic equations. \uc774\ucc28\ubc29\uc815\uc2dd\uc758 \ud574\ub97c \uad6c\ud558\ub294 \uac83\uc740 \uc21c\uc218 \uc218\ud559 \uc5ed\uc0ac\uc5d0 \uc788\uc5b4\uc11c \uac00\uc7a5 \uc624\ub798\ub41c \ubb38\uc81c \uc911 \ud558\ub098\uc600\ub2e4. The technique of solving such equations was discovered in ancient times in … \ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[11],"tags":[],"class_list":["post-3288","post","type-post","status-publish","format-standard","hentry","category-lectures"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"\uae40\uc601\uc6b1","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/ywkim","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3288","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/comments?post=3288"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3288\/revisions"}],"predecessor-version":[{"id":3289,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3288\/revisions\/3289"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3288"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3288"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3288"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}