Practice problems (MCQ Questions may have more than 1 correct answer) Q-1) Find the value of S, where Q-2) If be 2 complex numbers in the argand plane the n = a) b)|z_2| c) d)None of these Q-3) If , where , find the number of distinct elements in . Q-4)… Continue reading
Category: Complex Numbers
Week -2 | Complex Numbers – 4
Q-1) Show that Solution: Q-2) If , then find the value of the following series: Solution: Substituting in the equation we have We must remember that to represent a Complex Number in polar form, we take out the modulus from the algebraic form. On those lines we can say Thus the equation boils down… Continue reading
Week -1 | Complex Numbers – 3
1.1 Square Root of a Complex Number Let’s assume . Squarring both sides of the equation and comparing real and imaginary parts we have – (1) – (2) We also know . That implies . And thus finally taking the positive square root we arrive at: – (3). Comparing (1) & (3), we have & . Thus, depending… Continue reading
Week -1 | Complex Numbers – 2
1.1 Locus of a Complex Number In general, locus of a complex number defines the path that the complex number can travel under certain constraints. Mathematically, it is the set of all points on the Argand Plane (also called the Gaussian Plane) that satisfy a given mathematical relationship. For example, let’s consider a simple equation… Continue reading
Week – 1 | Complex Numbers – 1
1.1 Introduction A Complex Number is represented by a combination of 2 real values – across a 2D plane. The 2 axes form the ‘Real’ and ‘Imaginary’ axes, that are used to uniquely identify a Complex Number on the Complex plane – also called the Argand Plane. Thus an algebraic representation of is given by… Continue reading