Any complex number z = a+biz=a+bi has a trigonometric form
z = r(cos(theta) + isin(theta))z=r(cos(θ)+isin(θ))
where r = |z| = sqrt(a^2 + b^2)r=|z|=√a2+b2 and theta = tan^(-1)(b/a)θ=tan−1(ba)
For the given complex number, we have a = 3a=3 and b = 5b=5. Thus
r = sqrt(3^2 + 5^2) = sqrt(9+25) = sqrt(34)r=√32+52=√9+25=√34
and
theta = tan^(-1)(5/3) ~~ 59.04^@θ=tan−1(53)≈59.04∘
So we have the trigonometric form
3+5i = sqrt(34)(cos(tan^(-1)(5/3)) + isin(tan^(-1)(5/3)))3+5i=√34(cos(tan−1(53))+isin(tan−1(53)))
~~ sqrt(34)(cos(59.04^@) + isin(59.04^@))≈√34(cos(59.04∘)+isin(59.04∘))
