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Web skærmformat. - Aarhus Universitet

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VIII. Appendiks – 1. Polære koordinater og komplekse tal 514<br />

1.24. Potens på polarform<br />

Eksempel 6<br />

<br />

1 1<br />

Find +<br />

2 2<br />

☞ [S] Appendix I Complex numbers<br />

i<br />

10 .<br />

Løsning<br />

z = 1 1 1√<br />

π π<br />

+ i = 2(cos + isin<br />

2 2 2 4 4 )<br />

så<br />

z 10 √ 10 2<br />

= (cos 10<br />

2<br />

π<br />

+ isin 10π<br />

4 4 )<br />

= 25 5π 5π<br />

(cos + isin<br />

210 2 2 )<br />

= 1<br />

32 i<br />

1.25. Test komplekse tal<br />

Test<br />

Det komplekse tal z = (2cos π + 2isin π)<br />

☞ [S] Appendix I Complex numbers<br />

2 er:<br />

(a) z = 2. (b) z = −4. (c) z = 4.<br />

Afkryds den rigtige:<br />

(a) (b) (c)

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