Complex numbers problem

[Cholo]

I have tried to solve this problem, but couldnt, help would be appreciated

 

[Deleted member 4993]

View attachment 33398
I have tried to solve this problem, but couldnt, help would be appreciated

Please show us how you have tried to solve the problem.

If I were to solve this problem, I would

First write \(\displaystyle \frac{-3+3*i*\sqrt{3}}{1 + i}\) in a+bi form.​

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Then use DeMoivre's theorem.​

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[topsquark]

View attachment 33398
I have tried to solve this problem, but couldnt, help would be appreciated I

Please show us what you've tried. We can help you better that way.

I'd do things a bit differently than Subhotosh Khan. (But it's more or less the same method.) I'd find your argument in terms of the polar coordinate form [imath]\dfrac{-3 + i 3 \sqrt{3} }{1 + i} = r e^{i \theta }[/imath]. To my mind it's easier to think about how to take the powers.

Give it a try and if you need help with either method just let us know.

-Dan

 

[Dr.Peterson]

View attachment 33398
I have tried to solve this problem, but couldnt, help would be appreciated

Exactly what to do depends on what you've learned. You may not be familiar with the form [imath]re^{i\theta}[/imath], but know DeMoivre's theorem.

I myself would put both numerator and denominator in whatever version of polar form you know (because I see that both will work nicely), and do both the division and the powers using that.

We really need to see what method you have tried/learned, in order to see how to help.