New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2021 · 25 Jul · Shift 1 · Q45

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Complex Numbers
2021 · 25 Jul · Shift 1 · Q45

Complex Numbers question

2021 · 25 Jul · Shift 1 · Q45

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let

S = \left\{ {n \in N\left| {{{\left( {\begin{matrix} 0 & i \\ 1 & 0 \\ \end{matrix} } \right)}^n}\left( {\begin{matrix} a & b \\ c & d \\ \end{matrix} } \right) = \left( {\begin{matrix} a & b \\ c & d \\ \end{matrix} } \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

\underline{\hspace{2cm}}

.

Numerical answer

More from Complex Numbers

The equation of a circle is Re(z2) + 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, x2 $-$ 6x $-$ y + 13 = 0, has y-intercept equal to …2021 · Numerical
The equation $ar g (\frac{z - 1}{z + 1}) = \frac{π}{4}$ represents a circle with :2021 · MCQ
Let $z = \frac{1 - i 3}{2}$ , $i = - 1$ . Then the value of $21 + (z + \frac{1}{z})^{3} + (z^{2} + \frac{1}{z ^{2}})^{3} + (z^{3} + \frac{1}{z ^{3}})^{3} + .... + (z^{21} + \frac{1}{z ^{21}})^{3}$ …2021 · Numerical
If $(3 + i)^{100} = 2^{99} (p + i q)$ , then p and q are roots of the equation :2021 · MCQ
The least positive integer n such that $\frac{( 2 i ) ^{n}}{( 1 - i ) ^{n - 2}}, i = - 1$ is a positive integer, is .2021 · Numerical
Let z be those complex numbers which satisfy | z + 5 | $\leq$ 4 and z(1 + i) + $\overline{z}$ (1 $-$ i) $\geq -$ 10, i = $- 1$ . If the maximum value of | z + 1 |2 is $α$ + $β 2$ , then the value of ( $α$ + $β$ ) is …2021 · Numerical
If $S = {z \in C : \frac{z - i}{z + 2 i} \in R}$ , then :2021 · MCQ
Let z1 and z2 be two complex numbers such that $ar g (z_{1} - z_{2}) = \frac{π}{4}$ and z1, z2 satisfy the equation | z $-$ 3 | = Re(z). Then the imaginary part of z1 + z2 is equal to .2021 · Numerical