# Precalculus Formulae 6.5, 9.5-9.7

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 Author: tmartn22 ID: 301653 Filename: Precalculus Formulae 6.5, 9.5-9.7 Updated: 2015-04-27 21:30:29 Tags: complexnumbers demoivrestheorem parametrics conics polar Folders: Description: formula stuff Show Answers:

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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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