1

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 ______________.

Your input ____

2

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 sin

^{2}3$$\theta$$ + cos^{2}$$\theta$$ is equal to _______________.Your input ____

3

JEE Main 2021 (Online) 25th July Evening Shift

Numerical

+4

-1

The equation of a circle is Re(z

^{2}) + 2(Im(z))^{2}+ 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x^{2}$$-$$ 6x $$-$$ y + 13 = 0, has y-intercept equal to ______________.Your input ____

4

JEE Main 2021 (Online) 25th July Morning Shift

Numerical

+4

-1

Let $$S = \left\{ {n \in N\left| {{{\left( {\matrix{
0 & i \cr
1 & 0 \cr
} } \right)}^n}\left( {\matrix{
a & b \cr
c & d \cr
} } \right) = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)\forall a,b,c,d \in R} \right.} \right\}$$, where i = $$\sqrt { - 1} $$. Then the number of 2-digit numbers in the set S is _____________.

Your input ____

Questions Asked from Complex Numbers (Numerical)

Number in Brackets after Paper Indicates
No. of Questions

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