Trigonometric form is rcosθ+irsinθ=5+5i.
In Cartesian coordinates, x=5 and y=5. These make a right isosceles triangle, so θ=π/4 (45°) (tanθ=5/5=1).
sin(π/4)=cos(π/4)=½√2. rcos(π/4)+irsin(π/4)=5+5i, rcos(π/4)=5=rsin(π/4), so r=5√2.
5+5i=5√2(cos(π/4)+isin(π/4)). (The point (5,5) represents the complex number 5+5i, where x is the real axis and y the imaginary axis.)