Using complex numbers to represent distances

[thomas49th]

Homework Statement

A man travels 12 kilometres northeast, 20 kilometres 30° west of north and finally
18 kilometres 60° south of west. Determine his position with respect to his starting point.

Homework Equations

Using complex numbers

z = a + ib

|z|(cosx°+sinx°)

The Attempt at a Solution

Well I thought about plotting these on a argand diagram and concatenating them with one another:

a = 12cos45 + i12sin45
b = 20cos30 + i20sin30
c = -60cos60 + -i60sin60 (im sure you could turn these into 30s)

I guessimated that the resulting vector should be somewhere in the top left quadrant?

Adding up the components and the cosine components and dividing one by the other, then taking the inverse tangent does no yeild the correct result.

Am I even going in the right direction?

Thanks
Thomas

 

[Mark44]

Instead of writing the vectors in polar form as you have done, write them in rectangular form, and then add them. Polar form of vectors is useful if you need to multiply vectors; rectangular form is useful if you need to add or subtract them.

 

[tiny-tim]

Hi thomas49th!

A man travels 12 kilometres northeast, 20 kilometres 30° west of north and finally
18 kilometres 60° south of west. Determine his position with respect to his starting point.
…
b = 20cos30 + i20sin30

No, that's 30° north of east.

 

[thomas49th]

Instead of writing the vectors in polar form as you have done, write them in rectangular form, and then add them. Polar form of vectors is useful if you need to multiply vectors; rectangular form is useful if you need to add or subtract them.

By rectangular do you mean Cartesian? :)

Hi thomas49th! No, that's 30° north of east.

So
b = 20cos150 + i20sin150?

Thanks :)

 

[Mark44]

By rectangular do you mean Cartesian? :)

Same thing.

So
b = 20cos150 + i20sin150?

Your vector above is 30 deg. north of west. You want 30 deg. west of north.

 

[tiny-tim]

Hi Thomas!

b = 20cos150 + i20sin150?

A man travels 12 kilometres northeast, 20 kilometres 30° west of north and finally
18 kilometres 60° south of west. Determine his position with respect to his starting point.

No, that's 30° north of west.

I don't understand why you're so bad at this exercise …

what keeps making you get the wrong answer?​