adamjg2004 adamjg2004

07-05-2022
Mathematics

contestada

If z = 3cis30°, z3 in rectangular form is _ + _i.

Please solve for the blanks.

Respuesta :

LammettHash LammettHash

07-05-2022

Given that

z = 3 cis(30°)

z = 3 (cos(30°) + i sin(30°))

by DeMoivre's theorem it follows that

z³ = 3³ (cos(3×30°) + i sin(3×30°))

z³ = 27 (cos(90°) + i sin(90°))

z³ = 27 (0 + i)

z³ = 0 + 27 i

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