Euler form and vectors: z = -4 + 4sqrt(i) / Getting Rex home

[Colts18]

Hi, I'm new to this site and I need some help.

I need help converting: z = -4 + 4<3>i to Euler's form.

The "< >" mean square root. I didn't know how to write the symbol on the computer. The "i" is the complex number.

I got.... 8e^i 120. Is that right?

Then I'm suppose to find all the cube roots for it. How do I do that?

The other things that is giving me trouble are vectors. Here is one of the problems.

Rex leaves his home and wanders 4 miles northeast, then decides he's going the wrong way and heads 2 miles west.

1) Find a vector from where Rex is to his home.

2) Use that vector to find how far from home he is.

3) What direction must Rex walk to return home?

4 ) If Rex's real destination was at vector w=3i+3j from his home:

What is the angle from the vector to where Rex is to the vector to where he should be?

How far is Rex from where he should be?
--------------------------------------------------------------------------------

I need some help badly. Thank you so much from helping me!

 

[pka]

Re: Euler form and vectors

\(\displaystyle z = - 4 + 4\sqrt 3 i\,,\,\left|z\right| = 8\,\& \,\arg (z) = \arctan \left( {-\sqrt 3}\right)+\pi\)

 

[Colts18]

Re: Euler form and vectors

So then I got that correct, right? Thanks for the help.

Do you know how to do the vector problem as well? I don't even know where to get started on that.

 

[stapel]

Rex leaves his home and wanders 4 miles northeast, then decides he's going the wrong way and heads 2 miles west.

He has gone four units along the line y = x.

Draw a right triangle with its base on the x-axis, its "height" parallel to the y-axis, and the forty-five degree angle at the origin. The hypotenuse obviously has length 4. What are the lengths of the base and height? (Note: These lengths are the same, which will make the equation generated by the Pythagorean Theorem simple to solve.)

These lengths, along the x- and y-axes, relate to your vector components for his first "leg". The second "leg" is the addition of a simple vector parallel to the x-axis. What does the sum of these vectors give you? :wink:

Eliz.