MereTeacher

JEE • NEET • FOUNDATION

JEE Previous Year Question

$If α is a complex number such that α^{2} - α + 1 = 0, then α^{2011} =$

Topic: JEE PYQ

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

A $1$
B $- α$
C $α^{2}$
D $α$

Correct answer: D

Solution

(d) α^{2} - α + 1 = 0 \Rightarrow α = \frac{1 \pm 1 - 4}{2} = \frac{1 \pm 3 i}{2} \Rightarrow α = - ω ∴ α^{2011} = (- ω)^{2011} = - ω = α

More Complex Numbers PYQs

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