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Let u=<3,6>, v=<-8,2> and w=<2,-1>
find:
a)3v+2w-1/3u
- <-8*3,2*3>+<2*2,-1*2>-<(1/3)*3,(1/3)*6>
- =<-24+4-1, 6-2-2>
- =<-21,2>
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Find the Vector AB if AB has for initial point <-8,2> and for end point<3,6>
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A complex number z is given in exponential form as:z=12ei2(pi)/3
z=12(cos2(pi)/3+isin2(pi)/3)
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convert this: z=12(cos2(pi)/3+isin2(pi)/3) to the rectangular form
- =12(-1/2+i sq. root of 3/2)
- =z=-6+i6 sq.root of 3
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let z=5 +12i=reitheta
Convert to the exponential form
- r2=52+122=25+144=169
- r=sq root of 169=13
- tan theta=b/a=12/5
- theta=tan-1(12/5)= 67.4
- z=13ei67.4
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convert z to polar form
z=13ei67.4
z=13(cos67.4+isin67.4)
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find z3
z=4e i2(pi)/3
z3=43ei3(2(pi)/3) =64ei2(pi) =64(cos2(pi)+isin2(pi)) =64(1+i0)=64 - z3 =64
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