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I have posted a question before with the same problem, but it was not answered. I solved half the problem. But I am confused about the rest. Can someone check my answer and help me figure out the answer? For some reason, I keep getting 7/2 for the second half, which is incorrect and not even an option.  Thank you ahead of time for your help! Greatly appreciate it. :)

 

 Nov 23, 2020
 #1
avatar+112533 
+3

 

Hint:

 

\(cis(\theta) = e^{i\theta}\)

 

Using this it is relatively easy to determine the answer.   

 

As  \(e^{i\theta}\div e^{i\alpha}=e^{i(\theta -\alpha)}\)

 Nov 24, 2020
 #2
avatar+133 
+1

I got 7π/6. Is that correct?

Spring  Nov 24, 2020
 #3
avatar+112533 
+2

No it is not.

 

What is theta?

What is alpha?

What is theta-alpha ?

Melody  Nov 24, 2020
 #4
avatar+112533 
+3

\(cis(\theta) = e^{i\theta}\\ cis(7\pi/6) \div cis(\pi/3)= e^{i(7\pi/6)}\div e^{i(\pi/3)}=etc\)

Melody  Nov 24, 2020
 #5
avatar+133 
+2

Well, to be quite honest, I am not 100% sure. I didn't learn it in class with the equation you provided me. 

So solving it to my ability with your equation, correct me if I am incorrect, I got 5π/6.

Also, is the 2√15/5 correct?

Thank you Melody for your time and patience in helping me figure this out. I am not the best at Pre-Calc/Trig! :)

Spring  Nov 24, 2020
 #6
avatar+112533 
+3

Yes the number out the front is correct.

 

How do you do       x^7 divided by   x^2   ?

 

Please answer quickly.

Melody  Nov 24, 2020
edited by Melody  Nov 24, 2020
 #7
avatar+133 
+2

Okay, thank you.

You subtract 7-2 to get 5. The answer is x^5.

Spring  Nov 24, 2020
 #8
avatar+112533 
+2

right!

 

x^7 divided by x^2 = x^(7-2)= x^5

When you do not understand what to do always convert to a simply but similar example and see what happens.

 

\(cis(\theta) = e^{i\theta}\\~\\ cis(7\pi/6) \div cis(\pi/3)\\= e^{i(7\pi/6)}\div e^{i(\pi/3)}\\ =e^{[(i(7\pi/6)-i(\pi/3)]}\\ =e^{i[(7\pi/6)-(\pi/3)]}\)

 

 

What is next?

Melody  Nov 24, 2020
 #9
avatar+133 
+2

Next, you subtract 7π/6 & π/3. When you subtract you get 5π/6.

 Nov 24, 2020
 #10
avatar+112533 
+2

yes so it will be

 

e^(i(5pi/6)  = cis 5pi/6

Melody  Nov 24, 2020
 #11
avatar+133 
+2

Wow! Thank you so much Melody. I greatly appreciate it! 😊

Spring  Nov 24, 2020
 #12
avatar+112533 
+2

So long as I have helped you to learn, I am pleased.    laugh

Melody  Nov 24, 2020
 #13
avatar+116126 
+3

Thanks, Melody  !!!!

 

cool cool cool

 Nov 24, 2020

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