Question

How do you convert `4+4i` to polar form?

Answer 1

`(4sqrt2,pi/4)`

Explanation:

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

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

`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)|)))`

Now 4 + 4i is in the 1st quadrant ,hence we must ensure that `theta` is an angle in the 1st quadrant.

here x = 4 and y = 4

`rArrr=sqrt(4^2+4^2)=sqrt32=4sqrt2`

and `theta=tan^-1(4/4)=tan^-1(1)=pi/4" angle in 1st quadrant"`

`rArr(4,4)=(4sqrt2,pi/4)" in polar form"`