Solving Complex Numbers in JEE Main


Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit. To solve complex number problems in JEE Main, it is important to have a clear understanding of the properties and operations involving complex numbers.


Here are some strategies to solve complex number problems effectively in the JEE Main exam:

1. Simplify the Expression:
- Combine like terms and simplify the expression to make it easier to work with.

2. Use Euler's Formula:
- Euler's formula states that e^(ix) = cos(x) + i*sin(x). This formula is extremely useful in simplifying complex number expressions.

3. Identify Conjugate Pairs:
- In many complex number problems, the conjugate pairs play a crucial role. The conjugate of a complex number a + bi is a - bi. Use the property (a + bi)(a - bi) = a^2 + b^2 to simplify expressions.

4. Apply De Moivre's Theorem:
- De Moivre's theorem states that (cos(x) + i*sin(x))^n = cos(nx) + i*sin(nx). This theorem is used to simplify expressions involving powers of complex numbers.

5. Use Properties of Modulus and Argument:
- The modulus of a complex number is its distance from the origin, and the argument is the angle it makes with the positive real axis. Utilize properties such as |z1 * z2| = |z1| * |z2| and arg(z1 * z2) = arg(z1) + arg(z2) to simplify expressions.

6. Practice with Past Year Papers:
- Solve complex number problems from previous years' JEE Main papers to familiarize yourself with the type of questions asked and to gain confidence in solving them.

7. Seek Clarification:
- If you encounter a complex number problem that you are unsure about, seek clarification from your teachers or fellow students. Discussing and understanding different approaches can help you solve the problem more effectively.

8. Time Management:
- Allocate sufficient time to practice solving complex number problems to improve your speed and accuracy.




Quadratic equations are an important topic in the JEE Main exam. Here are some strategies to solve quadratic equation problems effectively:

1. Understand the Nature of Roots:
- Determine the nature of the roots (real, complex, equal, or distinct) by calculating the discriminant (b^2 - 4ac). This information helps in solving the equation correctly.

2. Factorization Method:
- If the quadratic equation can be factored, use the factorization method to solve it. Express the equation in the form (x - r)(x - s) = 0 and find the values of x.

3. Quadratic Formula:
- Use the quadratic formula x = (-b ± sqrt(b^2 - 4ac))/(2a) to