Complex Numbers Class 11 Worksheet with Answers

Complex Numbers Worksheet for Class 11

Welcome to our dedicated worksheet on Complex Numbers for Class 11, designed to strengthen your understanding and mastery of complex numbers as part of your Class 11 maths curriculum. This comprehensive resource offers a variety of problems ranging from basic operations to more challenging applications of complex numbers. Accompanied by detailed answers, this worksheet serves as an excellent tool for both learning and revision.

In this Complex Numbers Class 11 PDF, you will encounter problems that not only enhance your computational skills but also deepen your conceptual understanding. Whether you are reviewing for exams or looking to solidify your grasp of the topic, these exercises are tailored to guide you through the complexities of complex numbers effectively.

For those of you studying Class 11 Complex Numbers, this worksheet aligns perfectly with your curriculum requirements, ensuring that all key concepts are covered. From finding the modulus and argument to performing operations such as addition, subtraction, multiplication, and division, each question is designed to challenge and engage.

Students focusing on Class 11 Maths Complex Numbers will find these exercises particularly beneficial. The problems are crafted to reflect the typical questions found in Class 11 assessments, providing a robust platform for practice.

Our Maths Class 11 Complex Numbers section includes a variety of problems that progressively build your ability to solve complex numbers efficiently. The provided solutions are thorough, offering step-by-step explanations to aid in your understanding.

Finally, the “Maths Complex Numbers Class 11 Solutions” included in this PDF are comprehensive and clear, ensuring that you have the necessary support to tackle complex numbers with confidence. These solutions align with the NCERT Solution for Class 11 Maths Chapter 5, providing reliable methods and insights as per the national curriculum. They also serve as a part of the broader NCERT Solution for Class 11 Maths, ensuring consistency and thoroughness in your learning process.

Complex Numbers Class 11 Worksheet With Answers CBSE

Question 1: Write the complex number 𝑧=3−4𝑖z=3−4i in polar form.

Question 2: Find the modulus and argument of the complex number 𝑧=1+𝑖z=1+i.

Question 3: Simplify the expression (2+3𝑖)+(4−5𝑖)(2+3i)+(4−5i).

Question 4: Subtract 5−3𝑖5−3i from 3+2𝑖3+2i and express the result in the form 𝑎+𝑏𝑖a+bi.

Question 5: Multiply (1+𝑖)(1+i) and (2−3𝑖)(2−3i). Express the result in standard form.

Question 6: Divide 4+3𝑖4+3i by 2−𝑖2−i and simplify it to the form 𝑎+𝑏𝑖a+bi.

Question 7: If 𝑧=4𝑖z=4i, find 𝑧2z2 and 𝑧3z3.

Question 8: Solve the equation 𝑧2+4=0z2+4=0 for 𝑧z.

Question 9: Express 1𝑖i1 in the form 𝑎+𝑏𝑖a+bi.

Question 10: Find the conjugate of the complex number 7−5𝑖7−5i.

Question 11: Calculate the absolute value of −3+4𝑖−3+4i.

Question 12: Determine 𝑧z if 𝑧‾=3−2𝑖z=3−2i and 𝑧+𝑧‾=10z+z=10.

Question 13: If 𝑧=5𝑒𝑖𝜋/4z=5eiπ/4, express 𝑧z in rectangular form.

Question 14: Solve 𝑧−2𝑖𝑧+2𝑖=𝑖z+2iz−2i=i for 𝑧z.

Question 15: Find the sixth roots of 11 and express them in polar form.

Question 16: If 𝑧=𝑥+𝑦𝑖z=x+yi satisfies 𝑧2+𝑧‾=0z2+z=0, find 𝑥x and 𝑦y.

Question 17: Simplify (1+𝑖)8(1+i)8 using De Moivre’s theorem.

Question 18: Express −25−25 in terms of 𝑖i.

Question 19: Calculate ∣3+4𝑖+5𝑖2∣∣3+4i+5i2∣.

Question 20: If 𝑧1=2+𝑖z1=2+i and 𝑧2=3−4𝑖z2=3−4i, find 𝑧1𝑧2−𝑧1‾z1z2−z1.

Answers:

1. 5(cos⁡(tan⁡−1(−4/3))+𝑖sin⁡(tan⁡−1(−4/3)))5(cos(tan−1(−4/3))+isin(tan−1(−4/3)))
2. Modulus = 22, Argument = 𝜋/4π/4
3. 6−2𝑖6−2i
4. −2−𝑖−2−i
5. −1−5𝑖−1−5i
6. 145+115𝑖514+511i
7. −16−16 and −64𝑖−64i
8. 𝑧=2𝑖,𝑧=−2𝑖z=2i,z=−2i
9. 0−𝑖0−i
10. 7+5𝑖7+5i
11. 55
12. 𝑧=7+2𝑖z=7+2i
13. 522+522𝑖252+252i
14. 𝑧=4z=4
15. 𝑒𝑖𝜋/3,𝑒2𝑖𝜋/3,1,𝑒−𝑖𝜋/3,𝑒−2𝑖𝜋/3,−1eiπ/3,e2iπ/3,1,e−iπ/3,e−2iπ/3,−1
16. 𝑥=0,𝑦=−12x=0,y=−21
17. 1616
18. 5𝑖5i
19. 55
20. 10−9𝑖10−9i