QUIZ 5.1B

We show | F dt | | F | dt.

By definition, F dt is a complex number. So we can set { 1 } = F dt.

By Property (2), r0 = {  2  }.  Each side is real, and when a complex number is real, it is the same as its real part. So by the Real Part Property,   r0 = {  3  }.

But Re (F cis (-0))  {  4  } = | F |.| cis (-0)| = | F |.

So r0 | F | dt,   providing a b.   Hence   | F dt | | F | dt.

Match the above boxes 1, 2, 3, 4 with the selections
(a)  F cis (-0) dt,  (b)  | F cis (-0) | ,  (c) r0 cis 0,  (d) Re (F cis (-0)) dt.

My solutions:

1.   ;  2.   ;  3.   ;  4.   .   Check