Maharashtra Board Class 11 Mathematics & Statistics — Flashcards for Quick Revision

A: A set is a collection of well-defined objects. Objects are well-defined when we can clearly determine whether an element belongs to the collection or not. Well-defined examples: • Days in a week: {Mo

A: **Roster Form:** A = {M, A, R, I, G, E} **Set-builder Form:** A = {x | x is a letter in the word MARRIAGE} **Note:** Even though 'A' appears twice in MARRIAGE, we write it only once in the set since

A: **Definition:** An open interval (a,b) contains all real numbers between a and b, but excludes the endpoints a and b. **(2, 7) in set-builder form:** (2, 7) = {x | x ∈ R, 2 < x < 7} **Number line re

A: A complex number is a number of the form z = a + ib, where a, b ∈ R and i = √(-1) with i² = -1. Example: z = 3 + 4i - Real part: Re(z) = 3 - Imaginary part: Im(z) = 4 Note: The set of complex number

A: Step 1: Recall the pattern of powers of i: i¹ = i, i² = -1, i³ = -i, i⁴ = 1 Step 2: For any positive integer n, divide n by 4: i^n = i^r where r is the remainder when n is divided by 4 Step 3: Divid

A: Condition: Two complex numbers are equal if and only if their corresponding real and imaginary parts are equal. z₁ = z₂ ⟺ a = c and b = d Example: If 3x + i(2y - 1) = 6 + 5i, find x and y. Step 1: