July 23rd, 2015, 01:16 PM  #1 
Newbie Joined: Jul 2015 From: manchester Posts: 7 Thanks: 0  Exponential form of Complex Number
Hello, I am stuck on a problem which I got out of an old Text Book I downloaded online. Stroud Engineering Mathematics 1st edition. It's to do with Complex Numbers but I didn't know which forum to put it in. I think my problem may relate more to the Geometry of the Unit Circle. Anyway the problem is "Express in Exponential Form z1 = 10_ 37.25degrees, and z2 = 10_322.75 degrees." I got the first question right: the answer is 10e^j0.650. It's the 2nd question I have a problem with. The text book gives an answer of 10e^j0.650. In hindsight I understand that as this 22nd angle is the negative of the first angle. I didn't spot that so I calculated theta in radians based on the anticlockwise angle of 322.75 degrees. I thought z2 would be 10e^j5.633. Why are the two answers different? 
July 23rd, 2015, 04:25 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,541 Thanks: 592 
For complex numbers, the angle is mod $\displaystyle 2\pi$. The two answers are equivalent.

July 24th, 2015, 12:33 AM  #3  
Newbie Joined: Jul 2015 From: manchester Posts: 7 Thanks: 0  Quote:
I have got e raised to a different power: The text book answer is e raised to j x 0.650 while I have e raised to j x 5.633 Sorry to be awkward, but I still don't understand. Perhaps they should be equivalent and I have done something silly in my calculation that I am not seeing. Could you possibly calculate the exponential form in the anticlockwise angle and show me the steps, and how it is equivalent to that generated by the clockwise (negative angle)?!! That way I should get it!  
July 24th, 2015, 12:44 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,248 Thanks: 887 
0.650+ 5.633= 6.283 which is $\displaystyle 2\pi$ to three decimal places.
Last edited by Country Boy; July 24th, 2015 at 12:48 PM. 
July 24th, 2015, 01:55 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,190 Thanks: 1649 
The angle is usually chosen to be in the interval (180°, 180°] or the equivalent in radians.


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complex, exponential, form, number 
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