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Category > Business & Finance Posted 22 May 2017 My Price 5.00

Let C be the set of complex numbers

Let C be the set of complex numbers. Define addition on C by (a+bi) + (a+di)=(a+c)+(b+d)i and define scalar multiplication by A(a+bi)=Aa+Abi for all real numbers A. Show that C is a vector space with these operations

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Status NEW Posted 22 May 2017 12:05 PM My Price 5.00

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file 1495455571-Answer.docx preview (344 words )
L-----------et -----------C b-----------e t-----------he -----------set----------- of----------- co-----------mpl-----------ex -----------num-----------ber-----------s. -----------Def-----------ine----------- ad-----------dit-----------ion----------- on----------- C -----------by -----------(a+-----------bi)----------- + -----------(a+-----------di)-----------=(a-----------+c)-----------+(b-----------+d)-----------i a-----------nd -----------def-----------ine----------- sc-----------ala-----------r m-----------ult-----------ipl-----------ica-----------tio-----------n b-----------y A-----------(a+-----------bi)-----------=Aa-----------+Ab-----------i f-----------or -----------all----------- re-----------al -----------num-----------ber-----------s A-----------. S-----------how----------- th-----------at -----------C i-----------s a----------- ve-----------cto-----------r s-----------pac-----------e w-----------ith----------- th-----------ese----------- op-----------era-----------tio-----------ns ----------- An-----------swe-----------r -----------The----------- ve-----------cto-----------r s-----------pac-----------e (-----------lik-----------e a-----------ll -----------vec-----------tor----------- sp-----------ace-----------s) -----------mus-----------t f-----------oll-----------ow -----------the----------- fo-----------llo-----------win-----------g a-----------xio-----------ms -----------(if----------- th-----------ey -----------are----------- re-----------al -----------vec-----------tor----------- sp-----------ace-----------s i-----------n C-----------): -----------For----------- al-----------l x-----------,y,-----------z i-----------n C-----------, a-----------nd -----------A,B----------- in----------- R -----------1) -----------(x -----------+ y-----------) +----------- z -----------= x----------- + -----------(y -----------+ z-----------) 2-----------) x----------- + -----------y =----------- y -----------+ x----------- 3)----------- Th-----------ere-----------
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