Find the best tutors and institutes for Class 11 Tuition
Q4:
Express the complex number $3(7 + i7) + i(7 + i7)$ in the form $a + ib$.
Solution :
Step 1: Application of Distributive Property
To simplify the complex expression $3(7 + i7) + i(7 + i7)$, we must first distribute the scalar and imaginary multipliers across the terms within the parentheses [Per the Distributive Property of Multiplication over Addition: $a(b + c) = ab + ac$].
$3(7 + i7) = (3 \times 7) + (3 \times i7) = 21 + 21i$
$i(7 + i7) = (i \times 7) + (i \times i7) = 7i + 7i^2$
Step 2: Substitution and Simplification of Powers of $i$
We recall the fundamental property of the imaginary unit, where $i^2 = -1$ [Per the definition of the Imaginary Unit in the Complex Number System].
Substituting $i^2 = -1$ into the second expanded expression:
$7i + 7(-1) = 7i - 7 = -7 + 7i$
Step 3: Combining the Terms
Now, we sum the results from Step 1 and Step 2 to achieve the form $a + ib$:
Expression $= (21 + 21i) + (-7 + 7i)$
Group the real parts and the imaginary parts separately [Per the Associative and Commutative properties of complex addition]:
$= (21 - 7) + (21i + 7i)$
$= 14 + 28i$
Visual Representation of the Complex Vector
Analytical Summary Table
| Operation | Resulting Expression |
|---|---|
| Initial Distribution | $21 + 21i + 7i + 7i^2$ |
| Substitute $i^2 = -1$ | $21 + 21i + 7i - 7$ |
| Combine Real Components | $21 - 7 = 14$ |
| Combine Imaginary Components | $21i + 7i = 28i$ |
Final Solution: $14 + 28i$
More Questions from Class 11 Mathematics Complex Numbers EXERCISE 4.1
- Q1: Express the complex number in the form $a + ib$.
- Q2: Express the complex number $i^9 + i^{19}$ in the form $a + ib$.
- Q3: Express the complex number $i^{-39}$ in the form $a + ib$.
- Q5: Express the complex number $(1 - i) - (-1 + i6)$ in the form $a + ib$.
- Q6: Express the complex number in the form $a + ib$.
- Q7: Express the complex number in the form $a + ib$.
- Q8: Express the complex number $(1 - i)^4$ in the form $a + ib$.
- Q9: Express the complex number in the form $a + ib$.
- Q10: Express the complex number in the form $a + ib$.
- Q11: Find the multiplicative inverse of the complex number $4 - 3i$.
- Q12: Find the multiplicative inverse of the complex number .
- Q13: Find the multiplicative inverse of the complex number $-i$.
- Q14: Express the following expression in the form of $a + ib$:
CBSE Solutions for Class 11 Mathematics Complex Numbers
Chapters in CBSE - Class 11 Mathematics
Top Tutors who teach Complex Numbers
Super Tutor
Varthur, Bangalore
15 yrs of
Exp
9 students
497 hrs of classes completed
1000
per hour
Online Classes
I have over ten years of experience in the field of accounts. I am an IELTS-certified professional and have completed advanced Spoken and General English courses from the British Council. I hold a master's degree in Commerce and am interested in teaching. I have worked for Accenture, Deloitte, AIG, and a government-owned company, National Insurance. These experiences have given me real-time experience and expertise in the field of accounts, which I am eager to share with my students. As an IELTS 9 band scorer, I teach accounts and English to students in grades eleventh and twelfth. I offer Spoken English classes only online, one-on-one and in batches of up to tenth students. Each class lasts two hours a day, the introductory course lasts one and a half months, while the advanced course takes fifteen months to complete. For Spoken English, it takes around twenty to thirty hours to complete the basic level and forty-five to fifty hours for the advanced level. I accept students aged eleven years and above. I design a lesson plan that includes storytelling concepts, real-life examples, and practical exercises. I follow the Cambridge syllabus for accounts, and for English, I use practical-oriented techniques. I also frequently use a whiteboard, video, and audio links to help my students learn, and I provide soft copies of the materials, assignments, and question-and-answer sets for accounts.
His expertise shines through the clear explanations, making accounting concepts accessible and fostering a positive learning experience."
Top Tutor
Vimanapura Krishna Nagar, Bangalore
6 yrs of
Exp
7 students
717 hrs of classes completed
600
per hour
Online Classes
Student's Home
In this competitive world education is the most important tool rather I say that it is sword by which one can win the competition.so I am in this field from last four years and teaching is my passion and even strength.My students are very happy with me in college as well as in tutions. Their results show it all. Students are always been encouraged to do studies one should not force them for the same.
Top Tutor
Mathara, Kozhikode
12 yrs of
Exp
3 students
917 hrs of classes completed
700
per hour
Online Classes
I can explain the concepts with clarity. I focus on solving numerical problems in Physics so that a student can learn better.
Top Tutor
Nerul Sector 20, Thane
16 yrs of
Exp
7 students
482 hrs of classes completed
1000
per hour
Online Classes
Student's Home
Tutor's home
I teach chemistry to IB, IGCSE,CIE, CBSE, ISC, ICSE, JEE and NEET students
Arun Sir is a very good teacher and and very patient when explaining concepts. He gives very many practice tests and material, and makes sure you retain all your concepts. I would recommend sir to anyone who wants to improve their marks on chemistry.
Top Tutor
Dilshad Garden, Delhi
4 yrs of
Exp
3 students
949 hrs of classes completed
260
per hour
Online Classes
I am a Chartered Accountant by profession and have been teaching Commerce subjects—primarily Accounting and Economics—for the past 4 years. I work with BCom/BSc students and CA aspirants, helping them build strong conceptual clarity and practical understanding. Teaching is my passion and hobby, and I focus on delivering quality education by maintaining small group sizes (2–3 students at a time). This allows me to give individual attention, ensuring that every student understands the concepts thoroughly and gains confidence. My teaching approach is practical-based, designed to bridge the gap between academic theories and real-world industry applications. I emphasize how concepts are applied in actual business environments—both in private and public sectors—so students can connect textbook knowledge to real scenarios. I prefer conducting online, individual sessions to provide personalized support and address each student’s learning style and pace. I teach using a whiteboard for clear and visual explanations. For CA students, I recommend specific books aligned with the syllabus. For Class 11 and 12, I rely on their existing school books but provide additional notes or references on request to avoid overloading them. While I haven't pursued awards in teaching, the positive feedback from my students and their academic success bring me immense satisfaction. My goal is to make learning effective, relevant, and engaging for every student I teach.
