Simplifying with Imaginary Numbers

In summary, the correct answer for the given problem is (2+.5i)e^(1+3i)x + (2-.5i)e^(1-3i)x. The attempt at a solution involved trying to simplify the expression further, but it was mentioned that there may have been a mistake in rewriting sqr(-36) as 3i instead of 6i. It was also suggested to use the complex conjugate to simplify and to apply Euler's formula to convert the complex factors to e to some power and then simplify further.
  • #1
McAfee
96
1

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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  • #2
I noticed that you rewrote sqr(-36) = 3i when it should be 6i perhaps this is where you went wrong.
 
  • #3
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
 
  • #4
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.
 
  • #5
Ok. thanks for the help. I'll try again.
 

1. What are imaginary numbers?

Imaginary numbers are numbers that involve the square root of -1, often represented by the letter "i". These numbers do not exist on the real number line but are useful in solving certain mathematical problems.

2. How do you simplify with imaginary numbers?

To simplify with imaginary numbers, you first need to convert any real numbers to their complex form, which is a number multiplied by "i". Then, you can combine like terms, distribute any coefficients, and simplify the resulting expression.

3. What is the purpose of simplifying with imaginary numbers?

Simplifying with imaginary numbers allows us to solve problems that involve complex numbers, such as in electrical engineering, physics, and other scientific fields. It also allows for more efficient and concise mathematical expressions.

4. Can you add or subtract imaginary numbers?

Yes, you can add or subtract imaginary numbers just like any other type of number. Simply combine like terms, and remember that "i" has its own set of arithmetic rules (i x i = -1).

5. How do you multiply or divide with imaginary numbers?

Multiplying or dividing with imaginary numbers follows the same rules as multiplying or dividing with real numbers. Just remember that "i" has its own set of arithmetic rules, and you may need to simplify further by combining like terms and converting back to the proper form.

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