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JEE Main Complex Numbers — practice questions

Explore 14 free Complex Numbers questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Complex Numbers questions and exercises with answers

Showing questions 1–14 of 14.

Which complex number has the larger modulus?Read the answer and worked solution →Spot the value that is NOT purely imaginaryRead the answer and worked solution →Real part or imaginaryRead the answer and worked solution →Modulus or conjugateRead the answer and worked solution →Type the complex termRead the answer and worked solution →Which operation obeys itRead the answer and worked solution →Pop what sits on the real axisRead the answer and worked solution →One word is wrongRead the answer and worked solution →Order the reason for extendingRead the answer and worked solution →Which one does not belongRead the answer and worked solution →Real or complex onlyRead the answer and worked solution →Spot the false statementRead the answer and worked solution →Which ones belongRead the answer and worked solution →Knock out the true statementsRead the answer and worked solution →

Worked practice questions

Which complex number has the larger modulus?

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Questions
  1. A
    3 + 4i (|z| = 5)
    B
    1 + i (|z| = √2)
    Higher value
    3 + 4i (|z| = 5)
  2. A
    5 + 12i (|z| = 13)
    B
    8 + 6i (|z| = 10)
    Higher value
    5 + 12i (|z| = 13)
  3. A
    −2 + 2i (|z| = 2√2)
    B
    3 + 0i (|z| = 3)
    Higher value
    −2 + 2i (|z| = 2√2)

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Spot the value that is NOT purely imaginary

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Questions
  1. Items
    1. i⁴
    2. 3i
    3. −5i
    4. 2i
    Reason
    i⁴ = 1, which is real, not imaginary.
    Odd item
    i⁴
  2. Items
    1. i²
    2. i
    3. −1
    4. i⁶
    Reason
    i is imaginary; the others all equal −1 (real).
    Odd item
    i

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Real part or imaginary

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Items
  1. Item
    Written Re z
    Category
    Real part
  2. Item
    Sits on the x-axis
    Category
    Real part
  3. Item
    The 2 in 2 plus i5
    Category
    Real part
  4. Item
    Written Im z
    Category
    Imaginary
  5. Item
    Sits on the y-axis
    Category
    Imaginary
  6. Item
    The 5 in 2 plus i5
    Category
    Imaginary
Categories
  1. Item
    Real part
  2. Item
    Imaginary
Instructions
Tap each description into the part of the number it names.
_Source: syllabus Mathematics, Ch 4 'Complex Numbers and Quadratic Equations'_

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