# verkefnablad02 - Línuleg algebra A og B(STÆ107G STÆ106G...

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Unformatted text preview: Línuleg algebra A og B (STÆ107G, STÆ106G, HAG105G) Verkefnablað 2 25.8.2011 1. Reiknið eftirfarandi. (a) (8 + 6i) + (3 + 2i). (b) (4 + 5i) − (6 − 3i). 2. Reiknið eftirfarandi. (a) √ −16 · √ −25. (b) (1 + 2i)(1 + 3i). (c) (3 − 7i)2 . (d) i37 . 3. Reiknið eftirfarandi. (a) (5 + 7i)(3 − 2i). (b) (8i)(1 − i). 4. Reiknið eftirfarandi. (a) (b) 2 − 5i 1 − 6i 1 + 5i 4 + 3i 5. Finnið raunhluta, þverhluta, samok, lengd og margföldunarandhverfu tvinntölunnar z = 2+4i. 6. Sýnið að samokatala summu (margfeldi) tveggja tvinntalna, z1 og z2 , sé jöfn summu (margfeldi) samokatalna z1 og z2 . 7. Finnið pólhnit eftirfarandi tvinntalna. (a) 3 + 4 i. (b) 1 − i. 8. Leysið eftirfarandi jöfnur. (a) (b) (3 + 4i)2 − 2(x − iy ) = x + iy . 1+i 1−i 2 + 1 = 1 + i. x + iy 9. Finnið allar þriðju rætur af 1. 10. Finnið allar þriðju rætur af i. 11. Teiknið alla punkta z = x + iy (a) |z | < 2. (b) |z − 2 + i| = 1 (c) sem uppfylla eftirfarandi skilyrði. |z + 1| = |z − i|. 12. Finnið allar rætur eftirfarandi margliða. (a) z 2 − 3z + 5. (b) z 4 − 2z 2 + 4. 13. Reiknið 1 1 √ +√ i 2 2 100001 . ...
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