Polar Coordinates

[jbeckton]

Hi, we did some simple excersizes with rectangular and polar coordinates and are now tasked with using matlab to do the calculations for us. This is my senior year in engineering and I haven't really used much Matlab since my freshmen year so it's a bit of a struggle. I have managed to get all of the other problem s in Matlab but am stuck with this last one. Any help would be greatly appreciated. Thanks in advance:

Perform the operation using polar coordinates, and express the result in standard rectangular form: (2+j)^2

I used the following function to convert 2+j to polar coordinates:



<DL class=codebox><DT><DD><CODE>>> [Theta_a, R_a] = cart2pol( real(2), imag(j) )

Theta_a =

0.4636


R_a =

2.2361</CODE>
</DD></DL>

So I now have the function is polar coordinates but I do not know how to square this function before converting ot back to rectangular coordinates uning this function:



<DL class=codebox><DT><DD><CODE>[x, y] = pol2cart(Theta_a, R_a);
new_a = x + y*i </CODE>
</DD></DL>

The answer should be: 5[cos(2theta) + j sin(2theta)], theta=tan^-1 (1/2)

Can anyone tell me what I need to do to square that function?

Thanks

[shwaip]

it's probably better to just write your own conversion, rather than use the matlab builtins. that way you can learn something.

for polar [ r e^(I theta) ] -> Cartesian (a+bI):
a=r*cos(theta);
b=r*sin(theta);

for cart -> polar:
r=sqrt((a.^2 + b.^2));
theta = atan2(b,a);

[jbeckton]

Thanks, that will help me get from polar to cartesian, but how do I perform the requested operation using polar coordinates?

This is what I tried and I think it is correct, can you confirm?

>> [Theta_a, R_a] = cart2pol( real(2), imag(j) )
Theta_a =
0.4636

R_a =
2.2361
>> r=2.2361
r =
2.2361
>> theta=.4636
theta =
0.4636
>> (r*exp(theta*j))^2
ans =
3.0005 + 3.9998i

[beatz]

Well, you could easily confirm it yourself by calcuting (2+j)^2.

(2+j)^2 = (2+j)(2+j) = (4+2j+2j-1) = (3+4j)

Rather large error in your result for my taste, however I don't know matlab that well.

[jbeckton]

As you can see Matlab has rounded r and theta, I was asking if anyone knew how to remedy this or if it is acceptable.

[shwaip]

rather than re-assigning the values to r and theta by typing them out, you can do:

r = R_a;
theta=Theta_a;