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Standard Form of Complex Numbers
z = a+bi
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Absolute Value of a Complex number
|z|=√(a²+b²)
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Trigonometric Form of a Complex Number
z=r(cosΘ +isinΘ), where a = rcosΘ, b=rsinΘ, and r=√(a²+b²), and tanΘ=b/a.
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Product of Two Complex Numbers in Trigonometric Form
z1z2=r1r2[cos(Θ1+Θ2)+isin(Θ1+Θ2)]
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Quotient of Two Complex Numbers in Trigonometric Form
z1 / z2=r1 / r2[cos(Θ1-Θ2)+isin(Θ1-Θ2)], where z2!=0
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DeMoivre's Theorem
- if z = r(cosΘ+isinΘ)
- zn=[r(cosΘ+isinΘ)]n = rn (cosnΘ+isinnΘ)
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Finding Roots of Complex Numbers
 (cos( +isin( )) where k =0, 1, 2, 3..., n-1.
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Motion Formula using Parametric Equations
- x=(V0cosΘ)t
- y=h+(V0sinΘ)t-4.9t2
- 4.9 if in meters, 16 if in feet
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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.
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Relationships to convert from polar to rectangular
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Relationships to convert from rectangular to polar
- r²=x²+y²
- tanΘ=
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