The Complex Plane (Cartesian Plane)

The complex plane (or Argand plane or Gauss plane) is defined as a way to represent complex numbers geometrically. Basically, it’s a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis. The Complex Plane Cartesian Plane…

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.                  …

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 process of mathematical induction can be used to prove a very important theorem in mathematics known as De Moivre’s theorem. The De Moivre Theorem formula is useful for finding powers and roots of complex numbers. The De Moivre Theorem example (cos a + i sin a)^n = cos na + i sin na, where n…

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…