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VIII. Appendiks – 1. Polære koordinater og komplekse tal 500 1.2. Komplekse tal ☞ [S] Appendix I Complex numbers Definition Ved et kompleks tal forstås et udtryk z = a + bi hvor a = Re z og b = Im z er reelle tal kaldet realdel og imaginærdel. i er den imaginære enhed, formelt identificeret med i = √ −1, altså i 2 = −1. To komplekse tal a + bi og c + di er ens, hvis a = c og b = d. Mængden af komplekse tal betegnes C. De reelle tal R identificeres med komplekse tal, hvis imaginærdel er 0. Det er et (overraskende) faktum, at de sædvanlige regneregler for reelle tal udvider meningsfuldt fra realdel til alle komplekse tal. 1.3. Komplekse plan ☞ [S] Appendix I Complex numbers Definition Talplanen R 2 med rektangulære koordinater (x,y) identificeres med de komplekse tal (komplekse plan, Argand planen) C ved 1 = (1,0) og i = (0,1), så a + bi = (a,b)
VIII. Appendiks – 1. Polære koordinater og komplekse tal 501 Im bi i 0 1 1.4. Komplekse plan ☞ [S] Appendix I Complex numbers Definition - fortsat x-aksen kaldes den reelle akse og y-aksen kaldes den imaginœre akse. Normen kaldes modulus eller absolut værdi. Eksempel a a+bi Re |a + bi| = a 2 + b 2 = |(a,b)| |3 − 4i| = 3 2 + 4 2 = √ 25 = 5
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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