Question about converting polar to rectangular in complex numbers

Thread Starter

hunterage2000

Joined May 2, 2010
487
I have a question I cant work out

If v=200V(rms) angle-(35) and i = 10A(rms) angle-(-20), calculate the impedance in rectangular form. Is it:

A 11.47 + j16.38
B 15.32 - j12.85
C 18.12 + j8.45
D 6.84 - j18.79
 

hgmjr

Joined Jan 28, 2005
9,029
I have a question I cant work out

If v=200V(rms) angle-(35) and i = 10A(rms) angle-(-20), calculate the impedance in rectangular form. Is it:

A 11.47 + j16.38
B 15.32 - j12.85
C 18.12 + j8.45
D 6.84 - j18.79
The topic of math on complex variables is well covered in the AAC ebook.

hgmjr
 

someonesdad

Joined Jul 7, 2009
1,583
You should be able to do this nearly in your head (i.e., without a calculator) from knowing the elementary rules of complex numbers in polar form. The impedance magnitude is 20 ohms and the angle is 55 degrees (assuming the angles are measured in degrees). Now 55 degrees is nearly 60 degrees and you should have the sine and cosine of 60 degrees memorized (sine is sqrt(3)/2 and cosine is 1/2). Assuming 60 degrees and converting to rectangular coordinates, we get one coordinate is about 17.3 and the other is about 10. If you know how the trig functions change, then the answer is obvious. There are only two possible answers in the above set of four and it's obvious which one it is (I'll let you work out the details).

Tiny Tim throws his calculator away! :p
 

S_lannan

Joined Jun 20, 2007
246
When it comes to working with complex numbers even the best calculators including my ti-89 have had a nasty habit of getting it wrong. Always use common sense when dealing with complex numbers. Eg 10 + j5 will always fall in a certain quadrant.
 

t_n_k

Joined Mar 6, 2009
5,455
When it comes to working with complex numbers even the best calculators including my ti-89 have had a nasty habit of getting it wrong. Always use common sense when dealing with complex numbers. Eg 10 + j5 will always fall in a certain quadrant.
Can you give an example that might go wrong? I have my HP35s feeling rather insulted by this rebuke!
 
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