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. For general values of the argument Notation: argz= θ. 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. This formula is applicable only if x and y are positive. Let us see how we can calculate the argument of a complex number lying in the third quadrant. Complex numbers are defined as numbers of the form x+iy, where x and y are real numbers and i = √-1. But the following method is used to find the argument of any complex number. Here, p and q are real numbers and \(i=\sqrt{-1}\). For example, 3+2i, -2+i√3 are complex numbers. 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. POLAR FORM OF A COMPLEX NUMBER. NCERT Solutions For Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are prepared by the expert teachers at BYJU’S. Ö3 respectively. In general one says arg(−1) = π+ 2kπ, where kmay be any integer. 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 ). The angle θis called the argument of the complex number z. Euler and De Moivres Theorem 5. 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. The argument is deﬁned in an ambiguous way: it is only deﬁned up to a multiple of 2π. and the argument of the complex number \( Z \) is angle \( \theta \) in standard position. Importance of Ch 5 Class 11 Maths Revision Notes for Complex Numbers and Quadratic Equations. Here we should take the principal value ofΘ. Cube Roots of Unity Argument of a Complex Number 4. All the class 11 maths chapter 5 revision notes have been made by Vedantu in accordance with the latest CBSE syllabus so that there is no mistake if changes have been created by the CBSE board. We have seen examples of argument calculations for complex numbers lying the in the first, second and fourth quadrants. Click hereto get an answer to your question ️ The argument of the complex number sin 6pi5 + i ( 1 + cos 6pi5 ) is The argument of a complex number is the angle that the vector and complex number make with the positive real axis. Example 4: Find the modulus and argument of \(z = - 1 - … the argument of −1 could be π, or −π, or 3π, or, etc. Complex Numbers Class 11 – A number that can be represented in form p + iq is defined as a complex number. 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. Complex Numbers Part-2 for JEE Main & Class 11 Maths, Problem Solving Tricks to Crack JEE Mains 2020 MathonGo. This is known as Polar form (Trigonometric form) of a Complex Number. E.g. These NCERT Solutions of Maths help the students in solving the problems quickly, accurately and efficiently. Also, BYJU’S provides step by step solutions for all NCERT problems, thereby ensuring students understand them and clear their exams with flying … 3Π, or −π, or, etc see how we can the. Maths Revision Notes for complex numbers and i = √-1 ) of a complex number are positive complex. Multiple of 2π number that can be represented in form p + iq is defined numbers... 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