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OPERACE S K.Č. V GON. TVARU

OPERACE S K.Č. V GON. TVARU. násobení a dělení: a = |a| . (cos α + i.sin α ) b = |b| . (cos β + i.sin β ). a . b = |a| . |b| . (cos ( α + β ) + i.sin ( α + β )). umocňování – Moivrova věta: a = |a| . (cos α + i.sin α ). a n = |a| n . (cos (n. α ) + i.sin (n. α )).

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OPERACE S K.Č. V GON. TVARU

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  1. OPERACE S K.Č. V GON. TVARU • násobení a dělení: a = |a| . (cos α + i.sin α) • b = |b| . (cos β + i.sin β) a . b = |a| . |b| . (cos (α + β) + i.sin (α + β)) • umocňování – Moivrova věta: a = |a| . (cos α + i.sin α) a n = |a| n. (cos (n.α) + i.sin (n.α))

  2. OPERACE S K.Č. V GON. TVARU Příklad 1: Určete a.b, a/b, b5, je-li dáno: a = 8.(cos 120° + i.sin 120°) b = 2.(cos 30° + i.sin 30°) a . b = 8 . 2 . (cos (120°+30°) + i.sin (120°+30°)) = = 16 . (cos 150° + i.sin 150°) = 4 . (cos 90° + i.sin 90°) b5 = 25. (cos (5.30°) + i.sin (5.30°)) = 32 . (cos 150° + i.sin 150°)

  3. OPERACE S K.Č. V GON. TVARU Příklad 2: Určete z = a4 . b2, je-li dáno: a = 3.(cos 80° + i.sin 80°) b = √2.(cos 260° + i.sin 260°) a4 = 34. (cos 240° + i.sin 240°) = 81 . (cos 240° + i.sin 240°) b2 = (√2 )2. (cos 520° + i.sin 520°) = 2 . (cos 160° + i.sin 160°) z = a4 . b2 = 162 . (cos 400° + i.sin 400°) = 162 . (cos 40° + i.sin 40°)

  4. OPERACE S K.Č. V GON. TVARU Příklad 3: Určete z = a3 / b5, je-li dáno: a = 9.(cos 140° + i.sin 140°) b = 3.(cos 110° + i.sin 110°) a3 = 93. (cos 420° + i.sin 420°) = 729 . (cos 60° + i.sin 60°) b5 = 35. (cos 550° + i.sin 550°) = 243 . (cos 190° + i.sin 190°) z = a3 / b5 = 3 . (cos (-130°) + i.sin (-130°)) = = 3 . (cos 230° + i.sin 230°)

  5. OPERACE S K.Č. V GON. TVARU Příklad 4: Určete z = a . b7, je-li dáno: - nejprve převedeme a na goniometrický tvar Im y |a| φ 3 Re x

  6. OPERACE S K.Č. V GON. TVARU Příklad 4: Určete z = a . b7, je-li dáno:

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