How do you convert 4+4i to polar form?
1 Answer
Jul 13, 2016
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"