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annethinkso 4
Postad: 23 jan 2023 19:36

The equation z^3=w has a root 3(cos30°+i sin 30°), find w.

The answer is given as 27i. I cannot get that.

Ture 10320 – Livehjälpare
Postad: 23 jan 2023 20:01

W = z3, since one root z1 is 3(cos30+isin30)

w is z13 = (3(cos30+isin30))3 = 33(cos(30*3)+isin(30*3)) (arguments are in degrees)

w= 27(cos(90)+isin(90)) = 27i

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