Precalculus Formulae 6.5, 9.5-9.7

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tmartn22
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301653
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Precalculus Formulae 6.5, 9.5-9.7
Updated:
2015-04-27 21:30:29
Tags:
complexnumbers demoivrestheorem parametrics conics polar
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formula stuff
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  1. Standard Form of Complex Numbers
    z = a+bi
  2. Absolute Value of a Complex number
    |z|=√(a²+b²)
  3. Trigonometric Form of a Complex Number
    z=r(cosΘ +isinΘ), where a = rcosΘ, b=rsinΘ, and r=√(a²+b²), and tanΘ=b/a.
  4. Product of Two Complex Numbers in Trigonometric Form
    z1z2=r1r2[cos(Θ12)+isin(Θ12)]
  5. Quotient of Two Complex Numbers in Trigonometric Form
    z1 / z2=r/ r2[cos(Θ12)+isin(Θ12)], where z2!=0
  6. DeMoivre's Theorem
    • if z = r(cosΘ+isinΘ)
    • zn=[r(cosΘ+isinΘ)]= rn (cosnΘ+isinnΘ)
  7. Finding Roots of Complex Numbers
    (cos( +isin()) where k =0, 1, 2, 3..., n-1.
  8. Motion Formula using Parametric Equations
    • x=(V0cosΘ)t
    • y=h+(V0sinΘ)t-4.9t2       
    • 4.9 if in meters, 16 if in feet
  9. Finding rectangular equations of parametric equations
    Solve for t in the x or y equation, then plug that value for t in whichever equation, x or y, that you didn't use.
  10. Relationships to convert from polar to rectangular
    • x = rcosΘ
    • y = rsinΘ
  11. Relationships to convert from rectangular to polar
    • r²=x²+y²
    • tanΘ=

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