# Homework Help: Using complex numbers to represent distances

1. Feb 22, 2010

### thomas49th

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
Using complex numbers

z = a + ib

|z|(cosx°+sinx°)

3. 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

2. Feb 22, 2010

### Staff: Mentor

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.

3. Feb 22, 2010

### tiny-tim

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

4. Feb 22, 2010

### thomas49th

By rectangular do you mean Cartesian? :)

So
b = 20cos150 + i20sin150?

Thanks :)

5. Feb 22, 2010

### Staff: Mentor

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

6. Feb 22, 2010

### tiny-tim

Hi Thomas!
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?​