1
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
If for the complex numbers z satisfying | z $$-$$ 2 $$-$$ 2i | $$\le$$ 1, the maximum value of | 3iz + 6 | is attained at a + ib, then a + b is equal to ______________.
2
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
A point z moves in the complex plane such that $$\arg \left( {{{z - 2} \over {z + 2}}} \right) = {\pi \over 4}$$, then the minimum value of $${\left| {z - 9\sqrt 2 - 2i} \right|^2}$$ is equal to _______________.
3
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 ___________.
4
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 ______________.
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