1
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
Let z1 and z2 be two complex numbers such that $$\arg ({z_1} - {z_2}) = {\pi \over 4}$$ and z1, z2 satisfy the equation | z $$-$$ 3 | = Re(z). Then the imaginary part of z1 + z2 is equal to ___________.
2
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
+4
-1
The least positive integer n such that $${{{{(2i)}^n}} \over {{{(1 - i)}^{n - 2}}}},i = \sqrt { - 1}$$ is a positive integer, is ___________.
3
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
Let $$z = {{1 - i\sqrt 3 } \over 2}$$, $$i = \sqrt { - 1}$$. Then the value of $$21 + {\left( {z + {1 \over z}} \right)^3} + {\left( {{z^2} + {1 \over {{z^2}}}} \right)^3} + {\left( {{z^3} + {1 \over {{z^3}}}} \right)^3} + .... + {\left( {{z^{21}} + {1 \over {{z^{21}}}}} \right)^3}$$ is ______________.
4
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
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 _______________.