# How do you convert -729  to polar form?

Apr 23, 2018

$- 729 = 729 \setminus {e}^{i \pi}$ magnitude 729, angle $\pi$.

#### Explanation:

I'll write numbers in polar form as $R {e}^{i \theta}$, meaning magnitude $R$, angle $\theta$. If you haven't gotten to that notation in class yet (from Euler's Formula), think of it as the polar coordinate pair $\left(R , \theta\right)$.

$- 729$ has magnitude $729$ and angle $\pi$ aka ${180}^{\circ}$. The fact that negative reals have angle $\pi$ is the true meaning of Euler's Identity, ${e}^{i \setminus \pi} = - 1.$

$- 729 = 729 \setminus {e}^{i \pi}$

That's $\left(729 , {180}^{\circ}\right)$ if that's how you write polar coordinates.