Find all cube roots of the complex number. Leare answer intrig form. 125(cos 255° +isin 255°)

Question

Question

math trigonometry

Answer 1

Answer #1

z=125(cos 255⁰+isin255⁰)

Z= 125e^(255i)

Cube roots

(125)^(1/3)(cos(255⁰+2πk/3)+isin(255⁰+2πk/3)), k=0,1,2

(125)^(1/3)(cos(255/3)+isin(255/3))=5(cos 85⁰+isin85⁰)

5(cos(360+255/3)+isin(360+255/3))=5(cos205⁰+isin205⁰)

5(cos325⁰+isin325⁰)

Answer 2

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