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Complex Numbers

106 Questions Start JEE Advanced Test
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1980 Q101 JEE Advanced MCQ
14 Mar 2026
The smallest positive integer n for which ${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$ is
A.
$n = 8$
B.
$n = 16$
C.
$n = 12$
D.
none of these
1980 Q102 JEE Advanced Numerical
14 Mar 2026
Find the real values of x and y for which the following equation is satisfied $\,{{(1 + i)x - 2i} \over {3 + i}} + {{(2 + 3i)y + i} \over {3 - i}} = i$
1979 Q103 JEE Advanced MCQ
14 Mar 2026
If the cube roots of unity are $1,\,\omega ,\,{\omega ^2},$ then the roots of the equation ${\left( {x - 1} \right)^3} + 8 = 0$ are
A.
$ - 1,1 + 2\omega ,\,1 + 2{\omega ^2}$
B.
$ - 1,1 - 2\omega ,\,1 - 2{\omega ^2}$
C.
$ - 1, - 1, - 1$
D.
None of these
1979 Q104 JEE Advanced Numerical
14 Mar 2026
If x + iy = $\sqrt {{{a + ib} \over {c + id}}} $, prove that ${({x^2} + {y^2})^2} = {{{a^2} + {b^2}} \over {{c^2} + {d^2}}}$.
1978 Q105 JEE Advanced Numerical
14 Mar 2026
Express ${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$ in the form x + iy.
1978 Q106 JEE Advanced Numerical
14 Mar 2026
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 = ${a^3} + {b^3}$.