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

1 Answer
Jul 13, 2016

(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"