हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा १२

Choose the correct alternative: If ω ≠ 1 is a cubic root of unity and (1 + ω)7 = A + Bω, then (A, B) equals - Mathematics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

If ω ≠ 1 is a cubic root of unity and (1 + ω)7 = A + Bω, then (A, B) equals

विकल्प

  • (1, 0)

  • (– 1, 1)

  • (0, 1)

  • (1, 1)

MCQ

उत्तर

(1, 1)

shaalaa.com
de Moivre’s Theorem and Its Applications
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Complex Numbers - Exercise 2.9 [पृष्ठ ९४]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 2 Complex Numbers
Exercise 2.9 | Q 19 | पृष्ठ ९४

संबंधित प्रश्न

Show that `(sqrt(3)/2 + "i"/2)^5 + (sqrt(3)/2 - "i"/2)^5 = - sqrt(3)`


Find the value of `[(1 + sin  pi/10 + "i" cos  pi/10)/(1 + sin  pi/10 - "i" cos  pi/10)]^10`


If 2 cos α = `x + 1/x` and 2 cos β = `y + 1/y`, show that `x/y + y/x = 2cos(alpha − beta)`


If 2 cos α = `x + 1/x` and 2 cos β = `y + 1/y`, show that `xy - 1/xy = 2"i" sin(alpha + beta)` 


If 2 cos α = `x + 1/x` and 2 cos β = `y + 1/y`, show that `x^"m" y^"n" + 1/(x^"m" y^"n")` = 2 cos(mα – nβ)


If 2cos α = `x + 1/x` and 2 cos β = `y + 1/x`, show that `x^"m"/y^"n" - y^"n"/x^"m"` = 2i sin(mα – nβ)


Solve the equation z3 + 27 = 0


If ω ≠ 1 is a cube root of unity, show that the roots of the equation (z – 1)3 + 8 = 0 are – 1, 1 – 2ω, 1 – 2ω2 


Find the value of `sum_("k" = 1)^8 (cos  (2"k"pi)/9 + "i" sin  (2"kpi)/9)`


If ω ≠ 1 is a cube root of unity, show that (1 – ω + ω2)6 + (1 + ω – ω2)6 = 128


If ω ≠ 1 is a cube root of unity, show that (1 + ω)(1 + ω2)(1 + ω4)(1 + ω8)….. (1 + ω2n) = 1


If z = 2 – 2i, find the rotation of z by θ radians in the counterclockwise direction about the origin when θ = `pi/3`


If z = 2 – 2i, find the rotation of z by θ radians in the counterclockwise direction about the origin when θ = `(2pi)/3`


Choose the correct alternative:

The product of all four values of `(cos  pi/3 + "i" sin  pi/3)^(3/4)` is


Choose the correct alternative:

If ω = `cis  (2pi)/3`, then the number of distinct roots of `|(z + 1, omega, omega^2),(omega, z + omega^2, 1),(omega^2, 1, z + omega)|` = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×