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Sektion 3.3

[Matematik/Kalkulus (Lindstroem)/Kapitel 3]

Opgave 1

Skriv tallene på formen $a + ib$:

a) $e^{i\pi/2} = e^0(cos \pi/2 + i sin \pi/2) = i$

b) $$ e^{-i\pi/4} = \\ e^0(cos -\pi/4 + i sin -\pi/4) = \\ \sqrt 2 /2 - i\sqrt 2 /2 $$

c) $$ e^{i23\pi/6} = \\ e^0(cos 23\pi/6 + i sin 23\pi/6) = \\ cos 11\pi/6 + i sin 11\pi/6 = \\ \sqrt 3/2 - i/2 $$

Opgave 2

Skriv tallene på formen $a + ib$:

a) $e^{2 + i\pi/3} = e^2(cos \pi/3 + i sin \pi/3) = e^2(1/2 + i\sqrt3/2)$

b) $$ e^{ln 3 - 3i\pi/4} = \\ e^{ln 3}(cos -3\pi/4 + i sin -3\pi/4) = \\ 3(cos 5\pi/4 + i sin 5\pi/4) = \\ 3(.\sqrt 2/2) - i3(\sqrt 2/2 ) $$

Opgave 1

Skriv tallene på formen $a + ib$:

a) $e^{i\pi/2} = e^0(cos \pi/2 + i sin \pi/2) = i$

b) $$ e^{-i\pi/4} = \\ e^0(cos -\pi/4 + i sin -\pi/4) = \\ \sqrt 2 /2 - i\sqrt 2 /2 $$

c) $$ e^{i23\pi/6} = \\ e^0(cos 23\pi/6 + i sin 23\pi/6) = \\ cos 11\pi/6 + i sin 11\pi/6 = \\ \sqrt 3/2 - i/2 $$

Opgave 2

Skriv tallene på formen $a + ib$:

a) $e^{2 + i\pi/3} = e^2(cos \pi/3 + i sin \pi/3) = e^2(1/2 + i\sqrt3/2)$

b) $$ e^{ln 3 - 3i\pi/4} = \\ e^{ln 3}(cos -3\pi/4 + i sin -3\pi/4) = \\ 3(cos 5\pi/4 + i sin 5\pi/4) = \\ 3(.\sqrt 2/2) - i3(\sqrt 2/2 ) \\ $$

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