Class 11 Complex Numbers and Quadratic Equations worksheet

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   i⁻³³ equals:

   1. i
   2. 1
   3. −1
   4. −i

   Answer

   (d) −i

   −33 = 4 × −9 + 3

2. 2.

   (6 + 5i)(5 + 4i) equals:

   1. 50 + 49i
   2. 30 + 20i
   3. 10 + 49i
   4. 10 − 49i

   Answer

   (c) 10 + 49i

   30 + 49i + 20i², and i² = −1

3. 3.

   The modulus of −12 − 5i is:

   1. 7
   2. 17
   3. 169
   4. 13

   Answer

   (d) 13

   √(12² + 5²) = √169

Section B · short answer

1. 4.

   Express (1 + 7i)(2 − 4i) in the form a + ib.

   Answer

   30 + 10i

   2 − 4i + 14i − 28i²

2. 5.

   Express (2 + 3i) ÷ (5 + 4i) in the form a + ib.

   Answer

   22/41 + (7/41)i

   multiply top and bottom by 5 − 4i; the denominator becomes 41

Section C · long answer

1. 6.

   If z₁ = 3 + 4i and z₂ = 3 + 4i, find (a) z₁ + z₂, (b) z₁ − z₂, (c) z₁z₂, (d) z₁ ÷ z₂.

   Answer

   (a) 6 + 8i; (b) 0; (c) −7 + 24i; (d) 1

   for (d), multiply top and bottom by 3 − 4i

Fresh sheets for your child

In the app, every Complex Numbers and Quadratic Equations sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.

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