The De Moivre’s Theorem

A complex number is an expression of the form x + iy where x, y∈R We denote the set of complex numbers by C (Here i denotes √−1 so that i^2 = −1.). We can represent C as the Argand diagram or complex plane by drawing the point x + iy ∈C as the point…

Complex multiplication is not a difficult operation to understand from either an algebraic or a geometric point of view. We can do it algebraically first, and let’s take specific complex numbers to multiply, say 3 + 2i and 1 + 4i. Each has two terms, so when we multiply them, we’ll get four terms: (3…

Modulus is the length of a vector. The length is the distance between two points. To find the modulus of a complex numbers is similar with finding modulus of a vector. For a given complex number, z = 3-2i,you only need to identify x and y. Modulus is represented with |z| or mod z. In this…

The operation of complex numbers on Subtraction is simple in a way  that one have to do the normal subtraction Example: 1. (a-ib)-(c-id) . In this example, one is required to separate between Real part and Imaginary part. By doing so you’ll have (a-c)-i(b-d)  i.e (a-ib)-(c-id) = (a-c)-i(b-d)  Example: 2.                  …

We simply add the complex number of the form (a+ib)+(c+id) and get the two parts of Complex number i.e Real part, Re{z} and Imaginary part, Im{z}. If a + ib, c + id ∈ C then we can add and get as follows; (a + ib) + (c + id) = (a + c) +…

Complex plane can be thought to be modified Cartesian plane, with the real part of a complex number represented by a distance along the x-axis, and the imaginary part by a displacement along the y-axis. The concept of the complex plane allows a geometric interpretation of complex numbers. The real part of complex numbers is represented in the x-axis and Imaginary part…