In 3 + 4i the imaginary part is 4 and the modulus |z| comes out as 5, so this Class 11 complex-number sheet begins by separating the imaginary part from the whole. The key also gives the conjugate 2 − 3i and the result that i² lands on −1.
Key Takeaways
The imaginary part of 3 + 4i is 4 (Q1).
For z = 3 + 4i the modulus |z| is 5 (Q2).
The conjugate of 2 + 3i is 2 − 3i.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The imaginary part of the complex number 3 + 4i is:
(a) 3(b) 4(c) 4i(d) 5
2.If z = 3 + 4i, then the modulus |z| of z is:
(a) 7(b) 5(c) √7(d) 25
3.The conjugate of the complex number 2 + 3i is:
(a) -2 - 3i(b) -2 + 3i(c) 2 - 3i(d) 2 + 3i
4.The value of i² is:
(a) 1(b) -1(c) i(d) -i
5.The solutions of the equation x² + 1 = 0 are:
(a) 1 and -1(b) i and -i(c) i and i(d) Neither real nor complex
6.The multiplicative identity in the set of complex numbers is:
(a) 0(b) 1(c) i(d) 1 + i
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Express (3 + 2i) + (5 - i) in the form a + bi.
8.Express (2 + 3i)(1 - i) in the form a + bi.
9.Find the modulus of the complex number z = 1 + i.
10.Find the value of i¹⁰.
11.Solve the quadratic equation x² + 2x + 5 = 0.
12.Write the conjugate of the complex number z = 5 - 7i.
13.Express (1 + i)² in the form a + bi.
14.Find the sum of the roots of the equation x² - 5x + 6 = 0.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The roots of a quadratic equation are 2 and 3. Write the quadratic equation.
16.If the sum of the roots of the equation x² - kx + 6 = 0 is 7, find the value of k.
17.If the product of the roots of the equation x² - 3x + k = 0 is 10, find the value of k.
18.A rectangular garden has an area of 96 m² and a perimeter of 40 m. Find the length and breadth of the garden.
19.The sum of the squares of two consecutive natural numbers is 145. Find the two numbers.
20.If z = 1 + i, find z² and the modulus of z².
Answer Key
1. b) 4
2. b) 5
3. c) 2 - 3i
4. b) -1
5. b) i and -i
6. b) 1
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the imaginary part of 3 + 4i?
4, option (b) in this worksheet (Q1).
What is the modulus of z = 3 + 4i?
5, option (b) in this worksheet (Q2).
What is the conjugate of 2 + 3i?
2 − 3i, from the answer key on this page.
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