OpenStudy (anonymous):

Express the complex numbers in trigonmetric form.

2 years ago
OpenStudy (anonymous):

\[-6+6\sqrt{3}^{i}\]

2 years ago
OpenStudy (anonymous):

Help PLEASE

2 years ago
OpenStudy (anonymous):

Can you help me?

2 years ago
OpenStudy (irishboy123):

\(-6+6\sqrt{3} \, i\) \(-6(1-\sqrt{3} \, i)\) \(= -12(\dfrac{1}{2}-\dfrac{\sqrt{3}}{2} \, i)\) \(= -12(\cos(\dfrac{\pi}{3})-\sin(\dfrac{\pi}{3}) \, i)\)

2 years ago
OpenStudy (anonymous):

I got \[12(\cos(2\Pi/3) + i \sin(2\Pi/3)\]

2 years ago
OpenStudy (irishboy123):

cool, now i can mess about a bit \[= -12\left(\cos\dfrac{\pi}{3}-i \,\sin\dfrac{\pi}{3}\right) \] \[= -12e^{-i\frac{\pi}{3}}\] \[= +12.e^{i\pi}.e^{-\frac{\pi}{3}}\] \[= 12e^{i(\pi - \frac{\pi}{3})}\] \[= 12e^{i\frac{2\pi}{3}}\] \[=12\left(\cos\dfrac{2\pi}{3} + i \sin\dfrac{2\pi}{3}\right)\]

2 years ago
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