## anonymous one year ago Express the complex numbers in trigonmetric form.

1. anonymous

$-6+6\sqrt{3}^{i}$

2. anonymous

3. anonymous

Can you help me?

4. IrishBoy123

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

5. anonymous

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

6. IrishBoy123

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