Question

Express the complex number in trigonometric form.

-3 + 3 square root of 3i

Answer 1

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 2

@mathmath333 help?

Answer 3

is it this \(z=-3 + 3\sqrt{3i}\) or \(z=-3 + 3\sqrt{3}i\)

Answer 4

It doesn't say z = at all

Answer 5

look at right handside of z

Answer 6

This is what it looks like

Answer 7

ok
\(\large \tt \begin{align} \color{black}{z=a+bi\\~\\
r=|z|=\sqrt{a^2+b^2}\\~\\
\alpha=tan^{-1}(\dfrac{b}{a})\\~\\
trig form \\~\\
z=r(cos\alpha+isin\alpha)\\~\\
z=-3 + 3\sqrt{3i}\\~\\
r=\sqrt{(-3)^2+{(3\sqrt{3})}^2}=6\\~\\
\alpha=tan^{-1}\dfrac{3\sqrt{3}}{-3}=tan^{-1}(-\sqrt{3})=-\dfrac{\pi}{3}\\~\\
z=6[cos(-\dfrac{\pi}{3})+isin(-\dfrac{\pi}{3})]\\~\\

} \end{align}\)

Answer 8

Thank you so much!!

Answer 9

so which option choosed