Question

How do I convert the polar coordinates `3(cos 210^circ +i\ sin 210^circ)` into rectangular form?

Answer 1

You must multiply the modulus, `3`, by the values of the `cos` and `sin`, as:
`z=3cos(210°)+i3sin(210°)=`
to get the rectangular form: `z=a+ib`
`=-3sqrt(3)/2-i3/2`
Where:
`cos(210°)=-sqrt(3)/2`
`sin(210°)=-1/2`

Graphically you can see this as: