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VIII. Appendiks – 1. Polære koordinater og komplekse tal 506 For et kompleks tal z = a + bi er brøken z z ¯w z ¯w = = w w ¯w |w| 2 a + bi (a + bi)(c − di) = c + di c2 + d2 1.12. Kompleks brøk ☞ [S] Appendix I Complex numbers Eksempel 2 −1 + 3i Angiv på formen a + bi. 2 + 5i −1 + 3i 2 + 5i (−1 + 3i)(2 + 5i) = (2 + 5i)(2 + 5i) = (−1 + 3i)(2 − 5i) (2 + 5i)(2 − 5i) = (−2 + 15) + (5 + 6)i 2 2 + 5 2 = 13 11 + 29 29 i 1.13. Test komplekse tal ☞ [S] Appendix I Complex numbers
VIII. Appendiks – 1. Polære koordinater og komplekse tal 507 Test Det komplekse tal z = 2 1+i er: (a) z = 1 − i. (b) z = 2 − 2i. (c) z = 2 + 2i. Løsning 2 1 + i = = 2(1 − i) 2(1 − i) (1 + i)(1 − i) 1 2 + 1 2 = 1 − i Afkryds den rigtige: (a) (b) (c) 1.14. Kompleks kvadratrod ☞ [S] Appendix I Complex numbers Eksempel 3 For et positivt reelt tal c er hovedkvadratroden af −c √ −c = √ c i Løsningerne til ligningen x 2 + c = 0 er da ± √ −c.
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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