Question

How do you convert `3+2i` to polar form?

Answer 1

`(sqrt13,0.588)`

Explanation:

To convert from `color(blue)"cartesian to polar form"`

That is `(x,y)to(r,theta)`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(r=sqrt(x^2+y^2))color(white)(a/a)|)))`

and `color(red)(bar(ul(|color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|)))`

here x = 3 and y = 2

`rArrr=sqrt(3^2+2^2)=sqrt13`

Now, 3 + 2i, is in the 1st quadrant so we must ensure that `theta` is in the 1st quadrant.

`theta=tan^-1(2/3)=0.588" radians"larr" in 1st quadrant"`

Thus `(3,2)to(sqrt13,0.588)to(sqrt13,33.69^@)`