# How do you convert (2, 3pi/4) into cartesian form?

Dec 11, 2016

$- \sqrt{2} + \sqrt{2} i$

#### Explanation:

Currently the coordinate $\left(2 , 3 \frac{\pi}{4}\right)$ is in polar form, which is $\left(r , \theta\right)$ form.

We could use a funky looking graph like this in order to plot that point.

However, if we want to convert the coordinate into a more familiar rectangular or cartesian form, we need to get the coordinate into $a + b i$ form.

we can use the formula

$r \left(\cos \theta + i \sin \theta\right)$

to get the number into

$r \cos \theta + r \sin \theta i$

This is because $r \cos \theta$ is the horizontal component of the magnitude of $r$, and $r \sin \theta$ is the vertical component of $r$.

Plugging in for r and theta, in radians, we get

$- \sqrt{2} + \sqrt{2} i$

If we were to graph the point, we would do something like this, but instead of 2, we would plot the x axis at $- \sqrt{2}$, and similarly the y coordinate at $\sqrt{2}$