Sailing

[nycmathguy]

Section 6.5

Can you set up parts (a) and (b) to try on my own this weekend? Thanks.

 

[MathLover1]

a.
each ship as complex # (ai+bj)

b.

 

[Country Boy]

Since you are not using any property specific to complex numbers, it seems a bit silly to think of the vertical axis as an "imaginary axis". It is simpler to think of this as just a Cartesian coordinate system so that A is at (3, 4) rather than "3+ 4i" and B is at (-5, 2) rather than -5+ 2i.

In either case, the distance between them is sqrt((3- (-5))^2+ (4- 2)^2)= sqrt(64+ 4)= sqrt(68)= 2sqrt(17).

 

[MathLover1]

I agree that way is simpler, but problem states to use the vertical axis as an "imaginary axis"

 

[nycmathguy]

a.
each ship as complex # (ai+bj)

b.
View attachment 1996

I will try to do both parts using your hints.

 

[nycmathguy]

I agree that way is simpler, but problem states to use the vertical axis as an "imaginary axis"

Which way is simpler? Are you talking about Country Boy's suggestions?

 

[Country Boy]

I agree that way is simpler, but problem states to use the vertical axis as an "imaginary axis"

Then just replace "(a, b)" with "a+ bi".

 

[nycmathguy]

Then just replace "(a, b)" with "a+ bi".

Ha!

 

[nycmathguy]

a.
each ship as complex # (ai+bj)

b.
View attachment 1996

The book's answer for part (b) is as follows:

"Find the modulus of the difference of the complex numbers."

1. What's a modulus?

2. If my answer is wrong, why?

3. What does Ron Larson mean by his answer to part (b)?

 

[MathLover1]

1. the magnitude, it’s also called its length, or its absolute value
2. you need the difference of the complex numbers
3+4i-(-5+2i) =3+4i+5-2i=8+2i
To find modulus of a complex number z=a+bi we use formula:
|z|=sqrt(a^2+b^2)
you have a=8 and b=2
|z|=sqrt(8^2+2^2)=sqrt(68)=2sqrt(17)

 

[nycmathguy]

1. the magnitude, it’s also called its length, or its absolute value
2. you need the difference of the complex numbers
3+4i-(-5+2i) =3+4i+5-2i=8+2i
To find modulus of a complex number z=a+bi we use formula:
|z|=sqrt(a^2+b^2)
you have a=8 and b=2
|z|=sqrt(8^2+2^2)=sqrt(68)=2sqrt(17)

At least I got the distance right.