JEE Main & Advanced Maths Shortcuts and Tricks PDF Download

The JEE Main & Advanced Mathematics Shortcuts and Tricks PDF document comprises important formulae, tricks of algebra, and other methods which aim to make solving of mathematical problems faster. This information will be helpful during quick revisions and while practicing mathematics before taking the examination.

Mathematics is an integral part of the syllabus of the JEE Main and JEE Advanced examinations. It is vital for students to understand the concept and use the proper formula within limited time.

JEE Maths Tips, Tricks and Shortcut Methods

The JEE Mathematics Tricks PDF can be downloaded by students to practice important formulae and shortcuts for solving questions quickly in JEE Main and JEE Advanced exams.

👉 JEE Main & Advanced Maths Shortcuts and Tricks PDF Download

JEE Maths Shortcuts and Tricks Methods

Algebra contains several formulas and concepts that are useful for solving JEE Maths questions. The following tips and shortcut methods are based on the provided study material.

1. Rotation of a Complex Number

Multiplying a complex number z by i rotates its position through 90° anticlockwise in the complex plane without changing its magnitude.

Important Point:

• Multiplication by i represents a 90° anticlockwise rotation.

• The magnitude of the complex number remains unchanged.

• This property is useful in questions involving complex numbers and geometry.

2. Collinearity of Three Complex Numbers

If three complex numbers z₁, z₂, and z₃ represent collinear points, then the ratio

(z₃ − z₁)/(z₂ − z₁)

is a real number, provided z₁ and z₂ are distinct.

This property helps students check whether three points lie on a straight line in the complex plane.

3. Square Root of Complex Numbers

For the complex numbers 5 + 12i and 5 − 12i, the following shortcut identities are useful:

Formula 1:

√(5 + 12i) + √(5 − 12i) = 6

Formula 2:

√(5 + 12i) − √(5 − 12i) = 4i

These results use the principal square roots of the complex numbers.

4. Shortcut Method for Solving Complex Number Questions

In objective examinations such as JEE Main, students can use the option-checking method to solve certain complex number questions quickly.

For example, find the square roots of 5 − 12i.

Shortcut Solution:

Instead of solving the complete equation, square the given options and check which one gives 5 − 12i.

Consider:

(3 − 2i)² = 9 − 12i + 4i²

Since i² = −1,

= 9 − 12i − 4

= 5 − 12i

Therefore, the required square roots are ±(3 − 2i).

This method can save time in multiple-choice questions when the answer options are easy to verify.

Important Complex Number Formulas for JEE Main and Advanced

Complex Numbers is an important topic in JEE Mathematics. Students should revise the basic properties, identities, and geometric applications of complex numbers.

1. Cube Roots of Unity

Let ω be a non-real cube root of unity.

The important identity is:

1 + ω + ω² = 0

For a positive integer n:

• If n is a multiple of 3, then ωⁿ + ω²ⁿ = 2.

• If n is not a multiple of 3, then ωⁿ + ω²ⁿ = −1.

These identities are useful for simplifying expressions involving powers of complex numbers.

2. Area of a Triangle Using Complex Numbers

If a triangle has vertices represented by z, iz, and z + iz, its area is:

Area = ½|z|²

For example, let z = 1 + i.

Then:

iz = −1 + i

z + iz = 2i

Therefore:

Area = ½|1 + i|²

= ½ × 2

= 1 square unit

This formula helps students solve certain complex-number geometry questions without lengthy calculations.

3. Condition for an Equilateral Triangle

If z₁, z₂, and z₃ represent the vertices of a non-degenerate triangle, the triangle is equilateral when:

(z₁ − z₂)² + (z₂ − z₃)² + (z₃ − z₁)² = 0

This identity is useful in complex-number questions involving equilateral triangles.

4. Important Properties of Complex Numbers

Students should remember these basic properties while preparing for JEE Mathematics.

These formulas are useful for simplifying complex-number expressions and solving Algebra questions.

How to Use JEE Maths Shortcuts and Tricks for Exam Preparation?

Students can use shortcut techniques in solving Mathematics questions in JEE Main and Advanced exams in practice and revision sessions. However, it is crucial to understand the concepts behind each formula and not just use the shortcut technique without knowing how the technique works.

Do exercises that will need you to apply the shortcuts in different kinds of questions. Do past questions in JEE Main and Advanced exams to identify when using a shortcut will make your problem-solving process faster and when a more elaborate solution is required.

Revising formulas regularly and practicing many questions through mock tests could help improve your speed and accuracy.

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👉  JEE Main & Advanced Study Material