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Complex Numbers and Quadratic Equations

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Complex Numbers

Subtopic

Complex Numbers under Complex Numbers and Quadratic Equations for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the value of i101i^{101}?

    A.

    11

    B.

    −1-1

    C.

    ii

    D.

    −i-i

  2. 2.

    Find the imaginary part of the product (1+i)(1+i)(1 + i)(1 + i).

    A.

    00

    B.

    11

    C.

    22

    D.

    −2-2

  3. 3.

    What is the real part of the complex number z=frac11+iz = \\frac{1}{1+i}?

    A.

    11

    B.

    1/21/2

    C.

    −1/2-1/2

    D.

    00

Download the worksheet for Complex Numbers and Quadratic Equations - Complex Numbers to practice offline. It includes additional chapter-level practice questions.

Algebra of Complex Numbers

Subtopic

Algebra of Complex Numbers under Complex Numbers and Quadratic Equations for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the multiplicative inverse of 4−3i4 - 3i.

    A.

    4+3i25\frac{4+3i}{25}

    B.

    4−3i25\frac{4-3i}{25}

    C.

    4+3i7\frac{4+3i}{7}

    D.

    4+3i4+3i

  2. 2.

    The product of ii and −i-i is:

    A.

    11

    B.

    −1-1

    C.

    00

    D.

    i2i^2

  3. 3.

    Calculate the sum i5+i6+i7+i8i^5 + i^6 + i^7 + i^8.

    A.

    ii

    B.

    11

    C.

    00

    D.

    −1-1

Download the worksheet for Complex Numbers and Quadratic Equations - Algebra of Complex Numbers to practice offline. It includes additional chapter-level practice questions.

The Modulus and the Conjugate of a Complex Number

Subtopic

The Modulus and the Conjugate of a Complex Number under Complex Numbers and Quadratic Equations for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the modulus of z=i9z = i^9.

    A.

    00

    B.

    ii

    C.

    11

    D.

    −1-1

  2. 2.

    If z=4z = 4, then find its conjugate zˉ\bar{z}.

    A.

    −4-4

    B.

    44

    C.

    4i4i

    D.

    −4i-4i

  3. 3.

    The modulus of z=11−iz = \frac{1}{1 - i} is:

    A.

    11

    B.

    2\sqrt{2}

    C.

    12\frac{1}{\sqrt{2}}

    D.

    12\frac{1}{2}

Download the worksheet for Complex Numbers and Quadratic Equations - The Modulus and the Conjugate of a Complex Number to practice offline. It includes additional chapter-level practice questions.

Argand Plane and Polar Representation

Subtopic

Argand Plane and Polar Representation under Complex Numbers and Quadratic Equations for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If z=r(cos⁡θ+isin⁡θ)z = r(\cos \theta + i \sin \theta), then −z-z in polar form is:

    A.

    r(cos⁡(θ+π)+isin⁡(θ+π))r(\cos (\theta + \pi) + i \sin (\theta + \pi))

    B.

    r(cos⁡(−θ)+isin⁡(−θ))r(\cos (-\theta) + i \sin (-\theta))

    C.

    −r(cos⁡θ+isin⁡θ)-r(\cos \theta + i \sin \theta)

    D.

    r(cos⁡θ−isin⁡θ)r(\cos \theta - i \sin \theta)

  2. 2.

    What is the modulus of z=12−i32z = \frac{1}{2} - i\frac{\sqrt{3}}{2}?

    A.

    14\frac{1}{4}

    B.

    12\frac{1}{2}

    C.

    11

    D.

    3\sqrt{3}

  3. 3.

    If z=6z = 6, what is its representation in the Argand plane?

    A.

    (0, 6)

    B.

    (6, 0)

    C.

    (-6, 0)

    D.

    (6, 6)

Download the worksheet for Complex Numbers and Quadratic Equations - Argand Plane and Polar Representation to practice offline. It includes additional chapter-level practice questions.

Quadratic Equations with real coefficients

Subtopic

Quadratic Equations with real coefficients under Complex Numbers and Quadratic Equations for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the value of kk if the equation x2+k=0x^2 + k = 0 has roots ±6i\pm 6i.

    A.

    66

    B.

    3636

    C.

    −36-36

    D.

    1212

  2. 2.

    What are the roots of x2+18=0x^2 + 18 = 0?

    A.

    ±3i2\pm 3i\sqrt{2}

    B.

    ±2i3\pm 2i\sqrt{3}

    C.

    ±18i\pm 18i

    D.

    ±9i\pm 9i

  3. 3.

    Find the roots of x2+2x+17=0x^2 + 2x + 17 = 0.

    A.

    −1±4i-1 \pm 4i

    B.

    1±4i1 \pm 4i

    C.

    −2±8i-2 \pm 8i

    D.

    −1±16i-1 \pm 16i

Download the worksheet for Complex Numbers and Quadratic Equations - Quadratic Equations with real coefficients to practice offline. It includes additional chapter-level practice questions.

Complex Numbers and Quadratic Equations - Class 11 Maths (CBSE) | Krit.club