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 _______________.
Answer (integer)
1
Solution
Re $(z) = {{3 - 6{{\cos }^2}\theta } \over {1 + 9{{\cos }^2}\theta }} = 0$<br><br>$\Rightarrow$ $\theta$ = ${{\pi \over 4}}$<br><br>Hence, sin<sup>2</sup>3$\theta$ + cos<sup>2</sup>$\theta$ = 1.
About this question
Subject: Mathematics · Chapter: Complex Numbers and Quadratic Equations · Topic: Complex Numbers and Argand Plane
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