Summary EDEXCEL AS LEVEL FURTHER MATHEMATICS CORE PURE MATH

EDEXCEL AS LEVEL FURTHER MATHEMATICS CORE PURE
MATHS FORMULAE TO LEARN

im=m-m"ACCURATEmANSWER"mmm√-1

i²m=m-m"ACCURATEmANSWER"mmm-1

Conjugatemofmz=mam+mbim-m"ACCURATEmANSWER"mmmz*=mam-mbi

Ifmαmandmβmaremroots,mthemquadraticmequationmis...m-m"ACCURATEmANSWER"mmmz²m-
m(αm+mβ)zm+mαβm=m0

zm=mxm+myimcanmbemrepresentedmasmthemvector...m-m"ACCURATEmANSWER"mmm(x)
(y)monmthemArgandmdiagram

Modulusmofmzm=mxm+myim-m"ACCURATEmANSWER"mmm|z|m=m√x²m+my²

Argumentmofmzm=mxm+myim-m"ACCURATEmANSWER"mmmtanθm=my/xm(θm=marg)

Ifmzmliesminmfirstmquadrantmthenmargmzm=m-m"ACCURATEmANSWER"mmmα

Ifmzmliesminmsecondmquadrantmthenmargmzm=m-m"ACCURATEmANSWER"mmmπm-mα

Ifmzmliesminmthirdmquadrantmthenmargmzm=m-m"ACCURATEmANSWER"mmm-(πm-mα)

Ifmzmliesminmfourthmquadrantmthenmargmzm=m-m"ACCURATEmANSWER"mmm-α

|z₁z₂|m=m-m"ACCURATEmANSWER"mmm|z₁||z₂|

|z₁/z₂|m=m-m"ACCURATEmANSWER"mmm|z₁|/|z₂|

arg(z₁z₂)m=m-m"ACCURATEmANSWER"mmmargm(z₁)m+margm(z₂)

arg(z₁/z₂)m=m-m"ACCURATEmANSWER"mmmargm(z₁)m-margm(z₂)

Circlemradiusmrmandmcentremz₁m=m-m"ACCURATEmANSWER"mmm|zm-m(z₁)|m=mr

Perpendicularmbisectormbetweenmz₁mandmz₂m-m"ACCURATEmANSWER"mmm|zm-mz₁|m=m|zm-
mz₂|

Halfmlinemfrommzmatmanglemθm=m-m"ACCURATEmANSWER"mmmargm(zm-mz₁)m=mθ

Formulamformthemsummofmthemfirstmnmnaturalmnumbersmis...m-
m"ACCURATEmANSWER"mmmn
∑mrm=m½mnm(nm+m1)m
mr=1

Tomfindmthemsummofmamseriesmthatmdoesmnotmstartmatmrm=m1,muse...m-
m"ACCURATEmANSWER"mmmnm______mn_____mk-1
∑f(r)m=m∑mf(r)m-m∑f(r)
mr=k___mr=1___mr=1

1/αm+m1/βm=m-m"ACCURATEmANSWER"mmm(αm+mβ)/αβ

1/αm+m1/βm+m1/γm=m-m"ACCURATEmANSWER"mmmαβm+mβγm+mαγ/αβγ