Complex Numbers
502 Questions
1978
JEE Advanced
Numerical
IIT-JEE 1978
Express ${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$ in the form x + iy.
Correct Answer: $$\,\left( {{1 \over {5 + 3\cos \theta }}} \right) + \left( {{{ - 2\cot \theta /2} \over {5 + 3\cos \theta }}} \right)i$$
1978
JEE Advanced
Numerical
IIT-JEE 1978
If x = a + b, y = a$\gamma $ + b$\beta $ and z = a$\beta $ +b$\gamma $ where $\gamma $ and $\beta $ are the complex cube roots of unity, show that xyz = ${a^3} + {b^3}$.
Correct Answer: Solve it.