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Class 11 Maths Study Material

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Complex numbers and Quadratic equations

The value of (1 + i)^8 + (1 - i)^8 is

a) 16
b) -16
c) 32
d) -32

✔Answer

Correct Answer Is : 32

Solution Is :

If (x + iy)^(1/3) = a + ib, then (x/a) + (y/b) is equal to

a) 4(a² + b²)
b) 4(a² - b²)
c) 4(b² - a²)
d) 2(a² + b²)

✔Answer

Correct Answer Is : 4(a² - b²)

Solution Is :

If [(1 + i)/(1 - i)]^m = 1, then the least integral value of m is?

a) 2
b) 4
c) 8
d) 6

✔Answer

Correct Answer Is : 4

Solution Is :

Modulus of [(3 + 2i)/(3 - 2i)] is?

a) 1
b) 2-Jan
c) 2
d) √2

✔Answer

Correct Answer Is : 1

Solution Is :

If z = [(3√7) + 4i]^2 [(3√7) - 4i]^3 , then Re(z) = ?

a) 79 * 3√7
b) (79)^2 (3√7)
c) (-4)(79)^2
d) None of these

✔Answer

Correct Answer Is : (79)^2 (3√7)

Solution Is :

For what values of x and y, the complex number (9y²) - 4 - 10xi and (8y² + 20i⁷) are conjugate of each other?

a) X = -2 , y = 2
b) X = -2 , y = -1
c) X = 2 , y = 2
d) X = 2 , y = -2

✔Answer

Correct Answer Is : X = -2 , y = 2

Solution Is :

(3 + 2isinθ)/(1 - 2isinθ) will be real, if θ = ? (where n is an integer)

a) 2nπ
b) Nπ + (π/2)
c) Nπ
d) Nπ/2

✔Answer

Correct Answer Is : Nπ

Solution Is :

The amplitude of (1 + √3i)/(1 + √3) is?

a) π/3
b) -π/3
c) π/6
d) -π/6

✔Answer

Correct Answer Is : π/3

Solution Is :

If y = cosθ + isinθ , then the value of [y + (1/y)]

a) 2cosθ
b) 2sinθ
c) 2cosecθ
d) 2tanθ

✔Answer

Correct Answer Is : 2cosθ

Solution Is :

If P, Q, R, S are represented by the complex numbers (4 + i), (1 + 6i), (-4 + 3i), (-1-2i) respectively, then PQRS is a ?

a) Rectangle
b) Square
c) Rhombus
d) Parallelogram

✔Answer

Correct Answer Is : Square

Solution Is :

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Class 11 Maths Study Material

Complex numbers and Quadratic equations

The value of (1 + i)^8 + (1 - i)^8 is

Correct Answer Is : 32

Solution Is :

If (x + iy)^(1/3) = a + ib, then (x/a) + (y/b) is equal to

Correct Answer Is : 4(a2 - b2)

Solution Is :

If [(1 + i)/(1 - i)]^m = 1, then the least integral value of m is?

Correct Answer Is : 4

Solution Is :

Modulus of [(3 + 2i)/(3 - 2i)] is?

Correct Answer Is : 1

Solution Is :

If z = [(3√7) + 4i]^2 [(3√7) - 4i]^3 , then Re(z) = ?

Correct Answer Is : (79)^2 (3√7)

Solution Is :

For what values of x and y, the complex number (9y2) - 4 - 10xi and (8y2 + 20i7) are conjugate of each other?

Correct Answer Is : X = -2 , y = 2

Solution Is :

(3 + 2isinθ)/(1 - 2isinθ) will be real, if θ = ? (where n is an integer)

Correct Answer Is : Nπ

Solution Is :

The amplitude of (1 + √3i)/(1 + √3) is?

Correct Answer Is : π/3

Solution Is :

If y = cosθ + isinθ , then the value of [y + (1/y)]

Correct Answer Is : 2cosθ

Solution Is :

If P, Q, R, S are represented by the complex numbers (4 + i), (1 + 6i), (-4 + 3i), (-1-2i) respectively, then PQRS is a ?

Correct Answer Is : Square

Solution Is :

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Correct Answer Is : 4(a² - b²)

For what values of x and y, the complex number (9y²) - 4 - 10xi and (8y² + 20i⁷) are conjugate of each other?