Question

Express the complex number in trigonometric form.

-3 + 3 square root of threei

three square root three times the quantity cosine of five pi divided by six plus i times sine of five pi divided by six
six times the quantity cosine of two pi divided by three plus i times sine of two pi divided by three
three square root three times the quantity cosine of two pi divided by three plus i times sine of two pi divided by three
six times the quantity cosine of five pi divided by six plus i times sine of five pi divided by six

Answer 1

So
\[ A) 3 \sqrt{3}(\cos(\frac{5 \pi}{6})+i \sin(\frac{5 \pi}{6})) \\ B) 6(\cos(\frac{2 \pi}{3})+i \sin(\frac{2 \pi}{3})) \\ C)3 \sqrt{3}(\cos(\frac{2 \pi}{3})+i \sin(\frac{2 \pi}{3})) \\ D) 6(\cos(\frac{ 5 \pi}{6})+i \sin(\frac{5 \pi}{6}))\]
sorry this took so long for me to write
it is just hard for me to read all of those words at once

Answer 2

so that is the correct translation in choices correct?

Answer 3

i can attach a picture of the answer choices

Answer 4

so that wasn't correct?

Answer 5

it was correct, I'm just bad at finding symbols on this website

Answer 6

you could do what we did last time and evaluate everything and see which choice simplies to the complex number -3+3sqrt(3) i
or
well \[-3+3 \sqrt{3} i \text{ can be represented by } r(\cos(\theta)+i \sin(\theta)) \\ \text{ where } r=\sqrt{(-3)^2+(3 \sqrt{3})^2} \]

Answer 7

or we could find r first then thetha