solved: Let z = c o s θ + i s i n θ . ( 1 0 . 1 ) Use de Moivre’s theorem to find expressions for z n and 1 z n for all ninN.

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  • Let z=cosθ+isinθ.
    (10.1) Use de Moivre’s theorem to find expressions for zn and 1zn for all ninN.
    (10.2) Determine the expressions for cos(nθ) and sin(nθ).
    (10.3) Determine expressions for cosnθ and sinnθ.
    (10.4) Use your answer from (10.3) to express cos4θ and sin3θ in terms of multiple angles.
    (10.5) Eliminate θ from the equations
    4x=cos(3θ)+3cosθ
    4y=3sinθ-sin(3θ)
    45

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