Answers to Selected Exercises

Chapter 1

1.  geometric definition: vw=|v||w|cos(anglebetweenvandw)

component formula: vw=v1w1+v2w2+v3w3

Chapter 6

7a.  2

7b.  3

7c.  13

7d.  Arctan(32)

7e.  5+12i

7f.  213

7g.  313

10a.  Re[f(t)]=(1+t2)1,Im[f(t)]=t(1+t2)1

13a.  12

13b.  [a+aeaxcos(bx)+beaxsin(bx)](a2+b2)1

13c.  0

13d.  p2

16a.  1,i,1andi

16b.  1,exp(i2π3)=12[1+i3]andexp(i4π3)=12[1i3]

16c.  exp(iπ3)=12[1+i3],1andexp(i5π3)=12[1i3]

16d.  2exp(iπ3)=1+i3,2andexp(i5π3)=1i3

16e.  exp(iπ4)=12[1+i]andexp(i5π4)=12[1+i]

16f.  exp(i3π4)=12[1+i]andexp(i7π4)=12[1i]

16g.  exp(iπ6)=12[3+i], exp(i5π6)=12[3+i]and=i

Chapter 7

9b.  2

9b.  23

Chapter 9

5a.  fund.period = 2 ,fund ...

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