Education

# How to Learn De Moivre’s Identity for JEE

In 2022, the JEE Main exam was conducted in two sessions in June and July. The JEE Advanced exam will be conducted on 28 August by the IIT Bombay. Proper planning, determination, and hard work are necessary to crack this exam. JEE Advanced is tougher than any other engineering entrance exam in India.

Mathematics is a subject that some students find challenging to learn. But if learned thoroughly by understanding the basic concepts, it can be the easiest subject for them. Complex numbers is an easy and important chapter for JEE Mathematics. While learning this chapter, De Moivre’s theorem should never be left out. It is also known as De Moivre’s identity. Students should learn this theorem and practice the problems related to this theorem. They can definitely expect one question from this topic. Using this theorem, we can solve problems from trigonometry also.

## De Moivre’s Identity

The statement is given by (cos x + i sin x)n = cos nx + i sin nx, for any real number x. Here, n is a positive integer, and i is the imaginary part. The value of i is equal to the square root of -1.

Let us have a look at an example using this identity.

Example: If k = cos θ + i sin θ , then prove that kn + 1/kn = 2 cos nθ.

Solution:

Given k = cos θ + i sin θ

Using De Moivre’s identity, kn = cos nθ + i sin nθ

1/kn = k-n = cos nθ – i sin nθ

Adding the above equations,

kn + 1/kn = cos nθ + i sin nθ + cos nθ – i sin nθ

= 2cos nθ

Therefore, kn + 1/kn = 2 cos nθ

Hence proved.

### Things to Remember

As JEE is considered one of the toughest exams in India, students should never lose their confidence. Besides learning, they have to take care of some other things too. Mental and physical health is important to achieve success in any exam. Students should never forget to take enough rest. Proper sleep is essential for the students. Healthy food and water intake are essential for a healthy body. Learning for long hours is not recommended. They should take enough breaks in between. They are advised to participate in fun activities, watch TV shows etc. This will help them to relax and face the exam with confidence.

### Importance of JEE Notes

Making notes while learning is essential to score more marks. Students are recommended to make their notes so that they can easily refer to them during revision. They can also find JEE notes of each chapter online. While learning complex numbers, they should have a look at the complex numbers notes. This will help them revise all the important formulas, theorems, and questions asked from complex numbers in the previous year.

Students can visit BYJU’S to download JEE notes. They can also download the PDFs of the JEE notes for free. Previous yearS’ question papers with solutions, important formula PDFs, chapter-wise question papers and solutions, etc., are available on the website.

### Steve Tikilo 