Melody

yes so it will be

e^(i(5pi/6)  = cis 5pi/6

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?

Yes the number out the front is correct.

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

Please answer quickly.

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

No it is not.

What is theta?

What is alpha?

What is theta-alpha ?

You are welcome.  

Hint:

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

Using this it is relatively easy to determine the answer.   

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

Yes, i believe that is correct.

Joy buys some slices.  I don't know how many. So I will let the unknown number be represented by the letter X

Joy buys X slices.

How many does Ansan buy (answer in terms of X)

Then work your way through the other purchases.

Make an equation then solve it.

Give it a go and show us your logic so we can help you more  if you need it.

To other answerers: Please let asker guest answer this.

Please show us what you have attempted for yourself.