Complex Number Division Formula

Complex Number Division Formula

Complex Number Division Formula is a little more difficult than addition, subtraction, and multiplication of complex numbers because it is difficult to divide a number by an imaginary number. To better Complex Number Division Formula, students must find a term by which students can multiply the numerator and denominator and eliminate the imaginary part of the denominator, resulting in a real number in the denominator.

In this article, students will learn Complex Number Division Formula, divide complex numbers in polar form, divide imaginary numbers, and divide complex fractions.

Dividing Complex Numbers

To find the square root of a negative number, use the Complex Number. In the first century, Hero of Alexandria, a Greek mathematician, mentioned the Complex Number when attempting to find the square root of a negative number. He simply changed the negative to a positive and calculated the numeric root value. Furthermore, while searching for the negative roots of cubic and quadratic polynomial expressions in the 16th century, Italian mathematician Gerolamo Cardano defined the real identity of a Complex Number.

Complex Number is used in many scientific fields, including signal processing, electromagnetism, fluid dynamics, quantum mechanics, and vibration analysis. Students can learn about the Complex Number’s definition, terminology, visualization, properties, and operations here.

What is Dividing Complex Numbers?

Now that students have established what Complex Number Division Formula entails, let’s go over the steps involved. Follow the steps below to Complex Number Division Formula:

First, compute the conjugate of the complex number in the fraction’s denominator.

Multiply the conjugate by the complex fraction’s numerator and denominator.

In the denominator, use the algebraic identity (a+b)(a-b)=a2 – b2 and substitute i2 = -1.

Simplify by using the distributive property in the numerator.

Separate the resultant complex number’s real and imaginary parts.

Dividing Complex Numbers Formula

A complex number is the product of a real number and an imaginary number. These are the numbers that can be written in the form a+ib, where a and b are both real numbers. It is represented by the symbol z.

In complex number form, the value ‘a’ is known as the real part, which is denoted by Re(z), and ‘b’ is known as the imaginary part im. In the complex number form a +bi, ‘i’ is an imaginary number called “iota.”

Steps for Dividing Complex Numbers

To Complex Number Division Formula, follow these steps:

The procedure of splitting two complex numbers differs slightly from that of dividing two real numbers. It is the concept of rationalizing the denominator in fractions using irrational integers as denominators.

Step 1: Confirm that both the numerator and denominator are in the normal complex number form, i.e., z = a + ib.

Step 2: Determine the conjugate of the complex number in the fraction’s denominator. Assume the denominator is a + bi, and the conjugate is a bi.

Step 3: Multiply the numerator and denominator by the conjugate or both fraction terms.

Step 4: Using the distributive property, simplify the numerator.

Step 5: Using the difference of squares formula, simplify the denominator. Specifically, (a+b)(a-b) = a2 – b2

Step 6: Separate the real and imaginary elements of a complex number at the end.

This is how the Complex Number Division Formula is done.

Division of Complex Numbers in Polar Form

Students have a new sort of complex number representation known as the polar form of a complex number with the modulus and argument of a complex number, as well as its representation in the argand plane. In polar form, the complex number z = a + ib is represented by z = r (Cos + iSin).

Dividing Complex Numbers Examples

If pupils create a habit of returning to the mathematical exercises and solving the problems on a frequent basis. Students generally study the chapter and answer problems to understand more about the Complex Number Division Formula. After finishing this procedure, students begin working on the exercise involving the Complex Number Division Formula. There are several formulae related to the Complex Number Division Formula, and memorising all of the subtle phases is tough. When students have completed the problems connected to the topic of Complex Number Division Formula, they usually go to the following chapter.

When students have completed the problems connected to the topic of Complex Number Division Formula, they usually go to the following chapter. In general, the problems in the Complex Number Division Formula exercises are more difficult than in other chapters. And the Complex Number Division Formula has far-reaching effects. Students should be very attentive and meticulous when answering these chapters since the principles they acquire in the Complex Number Division Formula reverberate more in subsequent chapters.

Dividing Complex Numbers Practice Questions

One of the most crucial concepts for students to understand is the Complex Number Division Formula. The chapter has significant consequences and is one of the most often employed strategies.

Mathematics is one of the most significant disciplines that students study. Students frequently grasp the subject, which is generally due to rigorous preparation for the subject. Students cannot grasp the material overnight, and they must practise these ideas and chapters on a regular basis. The only method for pupils to learn the topic and the Complex Number Division Formula is to practise the problems on a regular basis.