If the real part of the complex number z = (3 + 2i cos θ)/(1 - 3i cos θ),θ (0,(π)/2) is zero, then the value of sin²3 θ + cos² θ is equal to _ _ _ _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Evening shift · Q30

JEE Main 202127 Jul, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

If the real part of the complex number

z = {{3 + 2i\cos \theta } \over {1 - 3i\cos \theta }},\theta \in \left( {0,{\pi \over 2}} \right)

is zero, then the value of sin²3

\theta

+ cos²

\theta

is equal to _______________.

Your answerType your answer. Integers and decimals are accepted.