Complex Numbers Class 11 – A number that can be represented in form p + iq is defined as a complex number. Complex numbers are defined as numbers of the form x+iy, where x and y are real numbers and i = √-1. Importance of Ch 5 Class 11 Maths Revision Notes for Complex Numbers and Quadratic Equations. For a complex number z = p + iq, p is known as the real part, represented by Re z and q is known as the imaginary part, it is represented by Im z of complex number z. For example, 3+2i, -2+i√3 are complex numbers. These NCERT Solutions of Maths help the students in solving the problems quickly, accurately and efficiently. For general values of the argument Usually we have two methods to find the argument of a complex number (i) Using the formula θ = tan−1 y/x here x and y are real and imaginary part of the complex number respectively. But the following method is used to find the argument of any complex number. E.g. Cube Roots of Unity POLAR FORM OF A COMPLEX NUMBER. Euler and De Moivres Theorem 5. NCERT Solutions for Class 11 Maths Chapter 5 NCERT Solutions of Exercise 5.2: Question 1 The Complex Number NCERT Solutions help students to understand the equations and formulas the are required to find the modulus and argument of the complex number Z= -1-i. Notation: argz= θ. Also, BYJU’S provides step by step solutions for all NCERT problems, thereby ensuring students understand them and clear their exams with flying … For a complex number z = x+iy, x is called the real part, denoted by Re z and y is called the imaginary part denoted by Im z. Click hereto get an answer to your question ️ The argument of the complex number sin 6pi5 + i ( 1 + cos 6pi5 ) is the argument of −1 could be π, or −π, or 3π, or, etc. The argument is defined in an ambiguous way: it is only defined up to a multiple of 2π. The angle θis called the argument of the complex number z. Here, p and q are real numbers and \(i=\sqrt{-1}\). We have seen examples of argument calculations for complex numbers lying the in the first, second and fourth quadrants. NCERT Solutions For Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are prepared by the expert teachers at BYJU’S. Let us see how we can calculate the argument of a complex number lying in the third quadrant. Note Since the above trigonometric equation has an infinite number of solutions (since \( \tan \) function is periodic), there are two major conventions adopted for the rannge of \( \theta \) and let us call them conventions 1 and 2 for simplicity. In general one says arg(−1) = π+ 2kπ, where kmay be any integer. Complex Numbers Part-2 for JEE Main & Class 11 Maths, Problem Solving Tricks to Crack JEE Mains 2020 MathonGo. Let OP = r, then x = r cos Θ , and y = r sin Θ => z = x + iy = r cos Θ + ir sin Θ = r ( cos Θ + i sin Θ ). Here we should take the principal value ofΘ. 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