EDEXCEL FURTHER MATHS CORE PURE YEAR 1 Test.

EDEXCEL FURTHER MATHS CORE PURE YEAR 1 TEST.

im=m-m"ACCURATEmANSWER"mm√-1

Imaginarymnumberm-
m"ACCURATEmANSWER"mmAmnumbermofmthemformmbi,mwherembm∈mR

Complexmnumberm-
m"ACCURATEmANSWER"mmWrittenminmthemformmam+mbi,mwherema,mbm∈mR

Linkingmimaginarymnumbersmtomdiscriminantm-m"ACCURATEmANSWER"mmIfmb²m-
m4acm<m0,mtheremaremnomrealmroots

Complexmnumbersmcanmbemaddedmormsubtractedmbym-
m"ACCURATEmANSWER"mmaddingmormsubtractingmtheirmrealmpartsmandmaddingmormsubtrac
tingmtheirmimaginarymparts

Youmcanmmultiplymamrealmnumbermbymamcomplexmnumbermbym-
m"ACCURATEmANSWER"mmmultiplyingmoutmthembracketsminmthemusualmway

Ifmb²m-m4acm<m0,mthenmthemquadraticmequationmax²m+mbxm+mcmhasm-
m"ACCURATEmANSWER"mmtwomdistinctmcomplexmroots,mneithermofmwhichmaremreal

i²m=m-m"ACCURATEmANSWER"mm-1

Principalmsquaremrootmofmamcomplexmnumberm-
m"ACCURATEmANSWER"mm√z,mhasmampositivemrealmpart

Formanymcomplexmnumbermzm=mam+mbi,mthemcomplexmconjugatemofmthemnumbermismdefi
nedmasm-m"ACCURATEmANSWER"mmz*m=mam-mbi

zmandmz*maremcalledm-m"ACCURATEmANSWER"mmamcomplexmconjugatempair

Youmcanmusemconjugatesmtom-m"ACCURATEmANSWER"mmdividemtwomcomplexmnumbers

Argandmdiagramm-m"ACCURATEmANSWER"mm-mRepresentsmcomplexmnumbers
-mx-axismismthemrealmaxismandmy-axismismthemimaginarymaxis
-
mzm=mxm+miymismrepresentedmbymthempointmP(x,y)mwheremxmandmymaremCartesianmcoor
dinates

Themcomplexmnumbermzm=mxm+miymcanmbemrepresentedmasm-
m"ACCURATEmANSWER"mmthemvectorm(xmy)monmanmArgandmdiagram

Modulusm-m"ACCURATEmANSWER"mmMagnitudemofmamcorrespondingmvector

Modulusmofmamcomplexmnumberm-m"ACCURATEmANSWER"mm|
z|,mdistancemfrommthemoriginmtomthatmnumbermonmanmArgandmdiagram.

Formamcomplexmnumbermzm=mxm+miy,mthemmodulusmismgivenmbym-
m"ACCURATEmANSWER"mm|z|m=mroot(x²m+my²)

Argumentmofmamcomplexmnumberm-
m"ACCURATEmANSWER"mmthemanglemitsmcorrespondingmvectormmakesmwithmthempositivemr
ealmaxis