Complex Numbers (Part 3/3) JEE Main PYQ + Theory | Prabhat Ranjan

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Complex Numbers (Part 3/3) JEE Main PYQ + Theory | Prabhat Ranjan

Complex Numbers Question 21-31 (Part 3/3) Class 11, 12 Mathematics Boards, JEE Main, JEE Advanced, IIT JEE Full course from basic JEE Main Question Practice JEE Main PYQ + Theory by Prabhat Ranjan for class 12, boards, IIT JEE 2025, JEE Main 2025, JEE Advanced 2025, IIT JEE 2026, JEE Main 2026, JEE Advanced 2026.

"Complex Numbers (Part 3/3) JEE Main PYQ + Theory" by Prabhat Ranjan concludes the comprehensive study of complex numbers, covering questions 21-31. This session is designed for Class 11 and 12 students aiming to excel in board exams and competitive exams like JEE Main and Advanced 2025 and 2026. It provides an in-depth exploration of complex numbers, with a focus on JEE Main previous year questions (PYQs), advanced theory, and problem-solving strategies. Key topics include complex numbers and quadratic equations, De Moivre's theorem, and other essential concepts, making it an essential resource for mastering complex numbers in both academic and competitive contexts.

All these aspects have been covered by Prabhat Ranjan in full detail in his new YouTube video.

I am Prabhat Ranjan, currently pursuing B.Tech in Mechanical Engineering from NIT Jamshedpur.

Timeline:
00:00 Introduction
01:45 21) If z = 2+3i, then z^5+(z)^5 is equal to
08:44 22) Let S = {z = x + iy : |z - 1 + i| ≥ | z |, | z | less than 2, |z + i| = |z-1|}. Then the set of all values of x, for which w= 2x + iy e S for some y € R , is
25:22 23) Let z1 = 2 + 3i and z2 = 3 + 4i . The set s = {z € C : |z - z,|2 |z Z2|2 = |z, - Z2|2} represents a [JEE-Main_25-01-2023_S1] (1) straight line with sum of its intercepts on the coordinate axes equals 14 (2) hyperbola with the length of the transverse axis 7 (3) straight line with the sum of its intercepts on the coordinate axes equals -18 (4) hyperbola with eccentricity 2
31:10 24) Let A=[(1)/(sqrt(10)) (3)/(sqrt(10)) (-3)/(sqrt(10)) (1)/(sqrt(10))] and B= [1 -i 0 1], where i=sqrt(-1). If M=A^(T)BA then the inverse of the matrix AM2023AT is
39:42 25) If the set {Re(z-z'+zz'/2-3z+5z') : z€C, Re(z)=3} is equal to Interval (a,b], then 24(b-a) equal to
48:52 26) If (1+i/1-i)^m / 2=(1+i/1-i)^n / 3=1(m, n ∈ N) then the greatest common divisor of the least values of m and n is
57:14 27) Let z be those complex numbers which satisfy |z + 5| ≤4 and z (1 + i) + z(1-i) ≥ 10,i -1. If the maximum value of |z + 1|2 is a + V2, then the value of (a +ß) is
01:10:43 28) The equation of a circle is Re(z2) + 2 (Im(z))2 + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x2 - 6x - y + 13 = 0, has y- intercept equal to
01:22:01 29) The least positive integer n such that (2i)n/(1-i)n-2 i=root-1 is a positive integer, is [JEE-Main_26-08-2021_S2]
01:29:08 30) Let Z1 and Z2 be two complex numbers such that arg (Z1 - Z2) = pi/4 and Z1, Z2 satisfy the equation |z - 3| = Re(z). Then the imaginary part of z1 + Z2 is equal to
01:36:09 31) Let S = {ZEC:z2+z=0} . Then sum of (Re(z)+Im(z)) is equal to

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