Complex Number Lecture-3 | Important Properties for WBJEE & JEE Main |Class 11| #mathematics #maths

Welcome to Lecture-3 of our Complex Number series for Class-11, specially designed for WBJEE & JEE Main aspirants! 📘 In this session, Ayan Sir will explain the Important Properties of Complex Numbers in a clear and student-friendly way. 📌 What you will learn today: Key properties of complex numbers Tricks to solve JEE & WBJEE level questions Real + Imaginary components Conjugate, Modulus, Argument, and more! 📚 Target Audience: Class 11 students preparing for WBJEE, JEE Main, and other competitive exams. 🔥 Stay tuned, take notes, and don’t forget to LIKE, SHARE & SUBSCRIBE for more such powerful sessions! 📅 LIVE Now 📍 Maths | Ayan Chakraborty Classes Solution: Q1). If z̅=-3+5i, then z= -3-5i [Option:A] Q2.) We have, Z=-2-√(-5)=-2-√(-1×5) [since, i=√-1] = -2-i√5 Therefore, z̅=-2+i√5=-2+√-5 [Option:A] Purely Imaginary Complex Number: Z=(a+ib) [where a, b ∈R] is said to be a Purely Imaginary Complex number if Re(Z)=0. Example: -7i=0-7i, 9i=0+9i Note: Z=(a+ib) is said to be a purely real number if Im(Z)=0. Example: 7= 7+0i, -6=-6+0i Q3). Let, Z =(a+ib)(c+id) Now, Z=(a+ib)(c+id) =ac+ad.i+bc.i-bd [i^2=-1] =(ac-bd)+i(ad+bc) Since, Z is a purely real number. Therefore, Im(Z)=0 So, ad+bc=0 or, bc+ad=0 [Option:D] Q4). Let Z= (a+ib)(x+iy) Now, Z= (a+ib)(x+iy) = ax+ay.i+bx.i-by =(ax-by)+i(ay+bx) Since, Z is a purely Imaginary number. Therefore, Re(Z)=0 So, ax-by= 0 [Option: B] Q5). [i^17 - (1/i)^34]^2 = [ i -(-1)]^2=(i+1)^2 =i^2+2.i.1+1=2i [Option:C] ❤Q6). The given question's answer is (1+i). [ Option:B] Q7). i^n+i^(n+1) + i^(n+2)+i^(n+3) =i^n(1+i+i^2+i^3) =i^n(1+i-1-i) = 0 [Option:A] Timestamp: 0:00 I think voice clear আছে 1:53 sin169 এর মান কত 2:37 Importing file... 4:14 Focus করো সবাই 4:54 Main concept বুঝে করবো 6:12 Angry Moment 7:03 Conjugate এর Important property 11:28 1st MCQ 12:56 2nd MCQ(Part 1) 13:15 Suparna Class গুলো দেখেছিস ? 14:20 একটু Wait কর না বাবু 14:30 Engaging Moment 15:59 কেউ বলো স্যার আমার GF বা BF আছে 17:45 2nd MCQ (part 2) 18:46 Sir Class 12 পড়াবেন না ! 19:45 কে Complex Number বা কে Complex Number নয়? 23:33 Purely Imaginary Number 26:25 3rd MCQ 30:06 4th MCQ 33:50 Properties of Addition 57:03 5th MCQ 1:03:35 6th MCQ 1:17:52 7th MCQ #ComplexNumber #Class11Maths #WBJEE2025 #JEEMain2025 #AyanSir #MathsLiveClass #ComplexNumberLecture #MathsForJEE #AyanChakraborty #OnlineMathClass #MathsLecture #ImportantProperties #JEEPreparation #wbjeepreparation