MereTeacher

JEE • NEET • FOUNDATION

JEE Previous Year Question

$If ω is a complex cube root of unity, then sin ((ω^{10} + ω^{23}) π - \frac{π}{4}) =$

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

A $1/ 2$
B $1/2$
C $1$
D $3 /2$

Correct answer: A

Solution

(a) sin ((ω^{10} + ω^{23}) π - \frac{π}{4}) = sin ((w + w^{2}) π - \frac{π}{4}) (∵ ω^{3} = 1) = sin (- π - \frac{π}{4}) = - sin (\frac{5 π}{4}) (∵ ω^{2} + ω + 1 = 0) = - (- \frac{1}{2}) = \frac{1}{2}

More Complex Numbers PYQs

$The conjugate of a complex number is \frac{1}{i - 1} . Then, that complex number is$
$If α is a complex number such that α^{2} - α + 1 = 0, then α^{2011} =$
$Let z_{0} be a root of a quadratic equation, x^{2} + x + 1 = 0 . If z = 3 + 6 i z_{0}^{81} - 3 i z_{0}^{93}, then arg z is equal t\dots$
$Let z be the complex number satisfying | z - 5 | \leq 3 and having maximum positive principal argument. Then\dots$
$If x = - 5 + 2 - 4, then the value of the expression x^{4} + 9 x^{3} + 35 x^{2} - x + 4 is A .Find - A .$