Quotient of Complex Number

[greatwhiteshark]

FIND: z/w
NOTE: d = degrees

z = 3(cos130d + i sin130d)

w= 4(cos270d + i sin270d)

MY WORK:


z = 3(cos130d + i sin130d)
--------------------------------
w= 4(cos270d + i sin270d)


z/w = 3/4 [cos(130d - 270d) + i sin(130d - 270d) ]

z/w = 3/4 [cos(-140d) + i sin(-140d) ]

z/w = 3/4 (cos320d + i sin320d)

BOOK"S ANSWER:

z/w = 3/4 (cos220d + i sin220d)

Where 220 degrees come from?

 

[Gene]

I would do some magic on w first.
w = 4(0+i(-1)) = -4i
z/w = 3(cos130d + i sin130d)/-4i =
3i(cos130d + i sin130d)/4 =
3i*e^(130*pi*i/180)/4
I don't recall your first z/w equation but...

 

[greatwhiteshark]

yes

Your notes are helpful.