New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2020 · 2 Sep · Shift 1 · Q32

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

PYQ Library
JEE Main
Mathematics
Complex Numbers
2020 · 2 Sep · Shift 1 · Q32

Complex Numbers question

2020 · 2 Sep · Shift 1 · Q32

JEE MainMathematicsComplex NumbersMCQ+4 / −1

The value of

{\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}

is :

A
${1 \over 2}\left( {\sqrt 3 - i} \right)$
B
- ${1 \over 2}\left( {\sqrt 3 - i} \right)$
C
$- {1 \over 2}\left( {1 - i\sqrt 3 } \right)$
D
${1 \over 2}\left( {1 - i\sqrt 3 } \right)$

More from Complex Numbers

The imaginary part of $(3 + 2 - 54)^{\frac{1}{2}} - (3 - 2 - 54)^{\frac{1}{2}}$ can be :2020 · MCQ
If $(\frac{1 + i}{1 - i})^{\frac{m}{2}} = (\frac{1 + i}{1 - i})^{\frac{n}{3}} = 1$ , (m, n $\in$ N) then the greatest common divisor of the least values of m and n is .2020 · Numerical
If z1 , z2 are complex numbers such that Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| , and arg(z1 - z2) = $\frac{π}{6}$ , then Im(z1 + z2 ) is equal to :2020 · MCQ
Let $u = \frac{2 z + i}{z - k i}$ , z = x + iy and k > 0. If the curve represented by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :2020 · MCQ
If a and b are real numbers such that $(2 + α)^{4} = a + b α$ where $α = \frac{- 1 + i 3}{2}$ then a + b is equal to :2020 · MCQ
If the four complex numbers $z, \overline{z}, \overline{z} - 2 Re o l imi t s (\overline{z})$ and $z - 2 R e (z)$ represent the vertices of a square of side 4 units in the Argand plane, then $∣ z ∣$ is equal to :2020 · MCQ
The value of $(\frac{- 1 + i 3}{1 - i})^{30}$ is :2020 · MCQ
The region represented by {z = x + iy $\in$ C : |z| – Re(z) $\leq$ 1} is also given by the inequality : {z = x + iy $\in$ C : |z| – Re(z) $\leq$ 1}2020 · MCQ