Category: Calculus

The reciprocal of complex numbers is helpful in the process of dividing one complex number with another complex number. The process of division of complex numbers is equal to the product of one complex number with the reciprocal of another complex number.. The reciprocal of the complex number z = a + ib is z−1=1a+ib=a−iba2+b2=aa2+b2+i(−b)a2+b2z−1=1a+ib=a−iba2+b2=aa2+b2+i(−b)a2+b2. This… Continue reading Reciprocal of a Complex Number

The following properties of complex numbers are helpful to better understand complex numbers and also to perform the various arithmetic operations on complex numbers. Conjugate of a Complex Number The conjugate of the complex number is formed by taking the same real part of the complex number and changing the imaginary part of the complex number to… Continue reading Properties of a Complex Number

With the modulus and argument of a complex number and the representation of the complex number in the argand plane, we have a new form of representation of the complex number, called the polar form of a complex number. The complex number z = a + ib, can be represented in polar form as z… Continue reading Polar Representation of a Complex Number

The angle made by the line joining the geometric representation of the complex number and the origin, with the positive x-axis, in the anticlockwise direction is called the argument of the complex number. The argument of the complex number is the inverse of the tan of the imaginary part divided by the real part of… Continue reading Argument of the Complex Number

The complex number consists of a real part and an imaginary part, which can be considered as an ordered pair (Re(z), Im(z)) and can be represented as coordinates points in the euclidean plane. The euclidean plane with reference to complex numbers is called the complex plane or the Argand Plane, named after Jean-Robert Argand. The complex number… Continue reading Graphing of Complex Numbers

The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers. We have the value of i2 = -1, and this is used to find the value of √-4 = √i24 = +2i  The value… Continue reading Power of i

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value ‘a’ is called the real part which is denoted by Re(z), and ‘b’ is called the imaginary part Im(z).  Also, ib… Continue reading What are Complex Numbers?

Complex numbers are helpful in finding the square root of negative numbers. The concept of complex numbers was first referred to in the 1st century by a greek mathematician, Hero of Alexandria when he tried to find the square root of a negative number. But he merely changed the negative into positive and simply took the… Continue reading Complex Number