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avatar+132 

If I am given a right triangle with legs 12 and 5, and a hypotenuse of 13, how to I find the complex number of e^(i*theta) in standard form a+bi? Theta represents the larger acute angle in this triangle. I don't understand because when I did tan^-1(12/5) on my calculator in radians, I get 1.176. But that's not right because it can't be made into a precise fraction and I have no idea how to put it in complex standard form

 Mar 7, 2023
 #1
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\(e^{i \theta} = \frac{5}{12} + \frac{13}{12} i\)

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 Mar 7, 2023
 #2
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e^(1.176i) = (5 / 13)  +  (12 / 13)i

 Mar 7, 2023
 #3
avatar+132 
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Oh yea, I forgot that e^{i \theta}= cos(\theta) +i sin(\theta). Thanks!
 Mar 10, 2023

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