Question

How do you convert `3+ j5` to polar form?

Answer 1

`(sqrt34,1.03)`

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 = 5

`rArrr=sqrt(3^2+5^2)=sqrt(9+25)=sqrt34`

Now 3 + 5j is in the 1st quadrant so we must ensure that `theta` is in the 1st quadrant.

`theta=tan^-1(5/3)=1.03" radians"larr " in 1st quadrant"`

Thus `(3,5)to(sqrt34,1.03)to(sqrt34,59.04^@)`