Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Algebra, Trigonometry & Geometry 🔹 Introduction What if exponentials, trigonometry, and complex numbers were all part of the same language? They are.And the key that connects them is the most elegant equation in mathematics: eiθ=cos⁡θ+isin⁡θ\boxed{e^{i\theta} = \cos\theta + i\sin\theta}eiθ=cosθ+isinθ​ This […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Calculus | Applications of Integration 🔹 What Is Definite Integration? Definite integration calculates the exact numerical value of an integral between two limits — representing the total accumulation or net area under a curve between two points. If f(x)f(x)f(x) is a continuous function […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Geometry & Algebra 🔹 Introduction Every complex number can be represented algebraically as z=x+iyz = x + iyz=x+iy.But there’s a more powerful way to express it — using length and angle instead of x and y. This is called the […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Algebra Meets Geometry 🔹 Introduction Complex numbers are more than just algebraic expressions — they represent points in a plane.This geometric representation is called the Argand Diagram. The Argand plane lets us see complex numbers — turning abstract algebra into […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Calculus | Integration Techniques 🔹 What Is Integration by Substitution? Integration by Substitution is the reverse process of the chain rule in differentiation. It’s used when the integral contains a composite function — something inside something else — and a direct integration approach […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Trigonometry & Geometry 🔹 Introduction Complex numbers are not just algebraic curiosities — they form a geometric system where algebra, trigonometry, and exponential functions meet beautifully. One result stands above the rest in uniting them: De Moivre’s Theorem. It transforms […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Calculus | Integration Techniques 🔹 What Is Integration by Parts? When differentiation involves a product rule, integration involves its reverse — and that’s exactly what integration by parts is. It allows us to integrate the product of two functions when direct integration isn’t […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Complex Numbers | Algebra & Geometry 🔹 Introduction Complex numbers connect algebra and geometry like nothing else in mathematics. Every complex number can be represented as a point or a vector on the Argand plane, and taking roots of complex numbers reveals beautiful […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)Published: October 2025Category: Calculus | Series Expansion | Applications of Differentiation 🔹 What Is a Maclaurin Series? The Maclaurin Series is a special form of the Taylor Series, where the expansion is centered at x=0x = 0x=0. It expresses a smooth function as an infinite polynomial, […]

Author: Rishabh Kumar (IIT + ISI | Global Math Mentor)**Published: October 2025Category: Vectors | 3D Geometry 🔹 Introduction In 3D geometry, lines and planes are the building blocks of space.Their equations in vector form provide an elegant, coordinate-free way to represent direction, position, and geometry. Every line is defined by a point and a direction,and […]