New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2006 · Shift 0 · Q68

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

PYQ Library
JEE Main
Mathematics
Complex Numbers
2006 · Shift 0 · Q68

Complex Numbers question

2006 · Shift 0 · Q68

JEE MainMathematicsComplex NumbersMCQ+4 / −1

The value of

\sum\limits_{k = 1}^{10} {\left( {\sin {{2k\pi } \over {11}} + i\,\,\cos {{2k\pi } \over {11}}} \right)}

is :

A
i
B
1
C
- 1
D
- i

More from Complex Numbers

If the cube roots of unity are 1, $ω, ω^{2}$ then the roots of the equation $(x - 1)^{3}$ + 8 = 0, are :2005 · MCQ
If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $∣ z_{1} + z_{2} ∣ = ∣ z_{1} ∣ + ∣ z_{2} ∣$ , then arg $z_{1}$ - arg $z_{2}$ is equal to :2005 · MCQ
If $ω = \frac{z}{z - \frac{1}{3} i}$ and $∣ ω ∣ = 1$ , then $z$ lies on :2005 · MCQ
Let z and w be complex numbers such that $\overline{z} + i \overline{w} = 0$ and arg zw = $π$ . Then arg z equals :2004 · MCQ
If $z = x - i y$ and $z^{\frac{1}{3}} = p + i q$ , then $\frac{( \frac{x}{p} + \frac{y}{q} )}{( p ^{2} + q ^{2} )}$ is equal to :2004 · MCQ
If $z^{2} - 1 = ∣ z ∣^{2} + 1$ , then z lies on :2004 · MCQ
If $z$ and $ω$ are two non-zero complex numbers such that $∣ z ω ∣ = 1$ and $A r g (z) - A r g (ω) = \frac{π}{2},$ then $\overline{z} ω$ is equal to2003 · MCQ
Let $Z_{1}$ and $Z_{2}$ be two roots of the equation $Z^{2} + a Z + b = 0$ , Z being complex. Further , assume that the origin, $Z_{1}$ and $Z_{2}$ form an equilateral triangle. Then :2003 · MCQ