Notation: argz= θ. Complex numbers are defined as numbers of the form x+iy, where x and y are real numbers and i = √-1. 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. Also, BYJU’S provides step by step solutions for all NCERT problems, thereby ensuring students understand them and clear their exams with flying … This is known as Polar form (Trigonometric form) of a Complex Number. Complex Numbers Class 11 – A number that can be represented in form p + iq is defined as a complex number. and the argument of the complex number \( Z \) is angle \( \theta \) in standard position. POLAR FORM OF A COMPLEX NUMBER. Argument of a Complex Number 4. Ö3 respectively. 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. Example 4: Find the modulus and argument of \(z = - 1 - … 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. But the following method is used to find the argument of any 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. NCERT Solutions For Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are prepared by the expert teachers at BYJU’S. Here we should take the principal value ofΘ. In general one says arg(−1) = π+ 2kπ, where kmay be any integer. Euler and De Moivres Theorem 5. 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. Let us see how we can calculate the argument of a complex number lying in the third quadrant. 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 ). For example, 3+2i, -2+i√3 are complex numbers. Click hereto get an answer to your question ️ The argument of the complex number sin 6pi5 + i ( 1 + cos 6pi5 ) is E.g. The argument of a complex number is the angle that the vector and complex number make with the positive real axis. Importance of Ch 5 Class 11 Maths Revision Notes for Complex Numbers and Quadratic Equations. Cube Roots of Unity This formula is applicable only if x and y are positive. 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. 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