Simplifying with Imaginary Numbers

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The discussion focuses on simplifying a mathematical expression involving imaginary numbers and exponential functions. The correct answer is identified as (2+.5i)e^(1+3i)x + (2-.5i)e^(1-3i)x. A participant points out an error in simplifying the square root of -36, suggesting it should be 6i instead of 3i. Suggestions for further simplification include using the complex conjugate to eliminate the complex number in the denominator and applying Euler's formula to combine the exponential factors. The original poster expresses gratitude for the assistance and plans to revise their solution.
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Homework Statement


I'm trying to see if what I have before the e match up with the correct answer.


the correct answer is (2+.5i)e^(1+3i)x + (2-.5i)e^(1-3i)x



The Attempt at a Solution


This is what I have so far.
serqC.png


I don't know how I would simplify anymore. Please help.
 
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I noticed that you rewrote sqr(-36) = 3i when it should be 6i perhaps this is where you went wrong.
 
jedishrfu said:
I noticed that you rewrote sqr(-36) = 3i when it should be 6i perhaps this is where you went wrong.

If you look and then divided it by 2 making it equal 3i
 
sorry, didnt notice the 2 divisor.

wrt simplifying, how about using the complex conjugate of -3+3i to multiply top and bottom that would eliminate the complex number denominator.

Also there's eulers formula so you could convert the complex factors to e to some power and then combine the powers and simplfy further.
 
Ok. thanks for the help. I'll try again.
 

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