Assignment:Analyzing Operationswith ComplexNumbers

| August 31, 2017

Question
Assignment:Analyzing Operationswith ComplexNumbers

Followthedirectionstosolveeachproblem.Besuretoshowallwork leadingtoyouranswer. Writeexplanationsfor youranswersusingcompletesentences.

.gif”>.gif”>.gif”>.gif”>1.Lookatthetable.Twocomplexnumbers,fand g, aregiveninthefirstcolumn.Thenextthree columnslistoperationstobeperformedusingthevariouspairsof fandg.Completethetable, leavingallsquareroots insimplifiedradicalform. Showallofyour work belowthetable.

Valuesof fandg

f+g

f×g

f

g

f=8+5i,g= 8-5i

f=-2+3i,g=-2-3i

f=7-i,g=7+i

2.Complexnumberpairs,suchasfandglistedinthetableabove,arecalledcomplex conjugates.Forexample,thecomplexnumbers(8+5i )and(8-5i )areconjugates.Describe

twopatternsrelatedtocomplexconjugatesyouseeinthetableinproblem1.

.gif”>3.Ploteachpairofconjugatesonthecoordinateplanebelow.Howarethepointsofeachpair related?Explainyouranswer.

4.Willtheabsolutevalueof acomplexnumberandits conjugatealwaysbeequal?Whyor why not?Explainyourreasoningusingthedefinitionof the absolutevalueofacomplexnumber.

5.Selecttwomorepatternsinvolvingcomplexconjugatestoinvestigate.Forexample,explore whathappenswhenyousubtractconjugates.Completethetablebywritingthreeconjugatepairs ofyourchoiceandtwopatternstoinvestigate.Showalloftheworkfor yourcalculations.

Valuesof fandg

FirstOperation

(Forexample,f-g)

SecondOperation

ComplexConjugatePair1

ComplexConjugatePair2

ComplexConjugatePair3

6.Whatpatternsdidyoudiscoverin problem5? Explainthepatternsyoufound.Ifyoudidnotfind anypatterns,explainwhyyouthinknonewerefound,

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