HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions

If ω is a complex cube root of unity, find the value of ω² + ω³ + ω⁴

If ω is a complex cube root of unity, find the value of (1 + ω²)³

If ω is a complex cube root of unity, find the value of (1 − ω − ω²)³ + (1 − ω + ω²)³

If ω is a complex cube root of unity, find the value of (1 + ω)(1 + ω²)(1 + ω⁴)(1 + ω⁸)

If α and β are the complex cube root of unity, show that α² + β² + αβ = 0

If α and β are the complex cube root of unity, show that α⁴ + β⁴ + α⁻¹β⁻¹ = 0

If , where α and β are the complex cube-roots of unity, show that xyz = a³ + b³.

Find the equation in cartesian coordinates of the locus of z if |z| = 10

Find the equation in cartesian coordinates of the locus of z if |z – 3| = 2

Find the equation in cartesian coordinates of the locus of z if |z − 5 + 6i| = 5

Find the equation in cartesian coordinates of the locus of z if |z + 8| = |z – 4|

Find the equation in cartesian coordinates of the locus of z if |z – 2 – 2i| = |z + 2 + 2i|

Find the equation in cartesian coordinates of the locus of z if `|("z" + 3"i")/("z" - 6"i")|` = 1

Select the correct answer from the given alternatives:

If ω is a complex cube root of unity, then the value of ω⁹⁹+ ω¹⁰⁰ + ω¹⁰¹ is :

If ω(≠1) is a cube root of unity and (1 + ω)⁷ = A + Bω, then A and B are respectively the numbers ______.

If α and β are complex cube roots of unity, prove that (1 − α)(1 − β) (1 − α²)(1 − β²) = 9.

Answer the following:

If ω is a complex cube root of unity, prove that (1 − ω + ω²)⁶ +(1 + ω − ω²)⁶ = 128

If ω is the cube root of unity then find the value of `((-1 + "i"sqrt(3))/2)^18 + ((-1 - "i"sqrt(3))/2)^18`

In how many different ways can 8 friends sit around a table?

A party has 20 participants. Find the number of distinct ways for the host to sit with them around a circular table. How many of these ways have two specified persons on either side of the host?